Rule -1-

In all preliminary rounds, judges must call back the number of couples requested by the Chairman. A preliminary round is any round in a section excluding the final. Examples are 1st Round, 2nd round, quarterfinal, and semi-final. The judges do not have to mark the competitors in any order. They simply indicate on their mark sheet the couples they wish to see in the next round. The judge must only mark as many couples as the Chairman requests. As an example in a semi-final of eleven dancers the Chairman may request that six couples be recalled to the final. Each judge should then recall six couples for each dance in the section.

No	A	B	C	D	E	F	G	Total
10		X	X	X		X		4*
11	X		X	X	X	X	X	6
12	X	X	X	X			X	4*
13						X	X	3
14	X	X			X	X		4*
15		X	X	X	X	X	X	6
16								0
17	X	X	X	X	X		X	6
18	X	X	X	X	X	X	X	7
19	X				X			2

The couples that advance to the next round are simply those with the most callback marks.  The scrutineer will add the marks together for each couple from all judges to find out who has advanced to the next round. It is not an uncommon occurrence for the scrutineer to not be able to call back the number of competitors requested by the Chairman.  Several couples may have received the same number of callback marks. The judges can all have provided the correct number of marks but the result just does not work out.  Take a semi-final of 11 couples with 6 couples requested for the final. Couples 11, 15, 17, and 18 are the couples with the highest marks.  Couples 10, 12, and 14 all have 4 callback marks.  The results therefore mean that 4 couples or 7 couples can be recalled, not the 6 that were requested.  The decision passes to the Chairman as to how many couples are recalled.  The Chairman alone makes the decision, not the scrutineer.

Rule -2-

In a final round all couples must receive a placement from each judge. A final round of a section can contain a maximum of eight couples. If more than eight couples have been recalled from a semi-final then a further preliminary round must be danced. In some cases even a round with eight couples must be danced as a semi-final. Again the Chairman alone makes the decision. Often a particular section will be danced as a straight final, meaning that there were not enough couples entered to require a preliminary round. Also in this situation organisers typically award, say, only 3 prizes for a section of 6 couples. The judges are still required to allocate a place to each and every couple on the floor.

Rule -3-

In a final round a judges first choice is marked “1,” second choice is marked “2,” third choice is marked “3,” and so on. Typically each judge has a different opinion as to the placement of the finalists. That is why we need the Skating System and scrutineers.

Rule -4-

In a final round a judge may not tie any couple for any place of any dance. Since the final round is intended to determine final placements a judge is not allowed to tie any couples. After applying the Skating System to the judge’s marks an unbreakable tie may result. This is not because the judge tied the couples but through the method by which the marks are tabulated. A possible cause of this is that the opinion of the judges differ because the ability of the couples vary wildly or are very similar to each other. Both of these extremes result in no clear-cut winner, runner-up, etc. The remaining seven rules are the ones that determine how the final result is calculated. It starts of simply and then gets progressively more complicated. The Skating System uses two concepts to arrive at a final result. The first is “majority” and the second is “overall performance.” A couple must convince a majority of the judges to mark them to win the dance. Furthermore they must achieve this in a majority of the dances making up the section for them to win the section. Obviously this does not always happen. The Skating System rules therefore define how to tabulate the results when there is no clear-cut winner either for an individual dance or for the section as a whole. The Skating System attempts to always reward overall performance. As we progress through these seven rules you will begin to understand why a couple that does not win any individual dance can win the section!!! Conversely a couple can win an individual dance and may only be placed 4th in the section.

Rule -5-

How to allocate positions in each dance. The Skating System is based on the marks a couple receives from a majority of judges.  The first and simplest step is to ascertain what makes up a majority.  A few examples should suffice, the majority of 3 is 2; the majority of 5 is 3; the majority of 7 is 4, and so on. We now tabulate each couple's marks in the final.  The next step is to place the winner by inspecting the marks for the number of 1st places.  It is important to note that in this rule we simply count the number of places, we do not add them together.  A couple’s results are 1,1,2,3,1,2,1; they have 4 1st places. The couple who has received the majority of 1st place marks is the winner of that dance and their marks have no further impact on the tabulation process.  The next step is to determine who is to be placed second.  This follows a similar process.  In this case, however, we count the number of “2nd place and higher marks” for the remaining couples.  The next step is to determine who is to be placed third.  We, similarly, count the number of “3rd place and higher marks” for each of the remaining couples.  This process is repeated until all couples have been placed. In the following simple example the positions are awarded as follows:

There are 5 judges so the majority is three.

	WALTZ
	Judges							Places																Result
No	A	B	C	D	E	F	G	1		1-2		1-3		1-4		1-5		1-6		1-7		1-8
51	1	1	1	2	1			4		---		---		---		---		---		---		---		1
52	4	2	2	1	2			1		4		----		----		----		---		---		---		2
53	3	3	3	5	4			---		---		3		----		----		---		---		---		3
54	2	4	5	4	3			---		1		2		4		----		---		---		---		4
55	5	6	4	3	5			---		---		1		2		4		---		---		---		5
56	6	5	6	6	6			---		---		---		---		1		5		---		---		6

1.	Count 1st places.  #51 has 4 first-place marks and #52 has 1.  The remaining couples have no first-place marks. #51 has attained a majority of first-place marks and is therefore is placed 1st.  Although #52 attained a first-place mark they have not been placed yet and therefore stay in the tabulation.
2.	Count “2nd and higher” (1st and 2nd) place-marks awarded to the remaining couples to place the 2nd position.  #52 has 4 “2nd and higher” place marks and #54 has 1.  #52 is therefore awarded the second place having achieved a majority of “2nd place and higher” marks.
3.	The same process is followed for “3rd and higher” to place the 3rd place and so on to the 6th place.

Rule -6-

More than one couple have a majority for the same place. There are 7 judges so the majority is 4.     1. 1st and 2nd places are awarded based on a simple majority (Rule 5).      2. When we count “3rd and higher places” both #63 and #64 have achieved a majority.  The greater majority has been attained by #63 and is, therefore, awarded 3rd place with #64 awarded 4th place.   WALTZ   Judges Places Result No A B C D E F G 1 1-2 1-3 1-4 1-5 1-6 1-7 1-8   61 1 1 2 1 4 2  1  4 ---- ---- ---- ---- ---- ---- ---- 1 62 6 2 1 5 2  1  2 2 5 ---- ---- ---- ---- ---- ---- 2 63 2 4 3 3 6  3  3 ---- 1 5 ---- ---- ---- ---- ---- 3 64 3 3 5 2 1  5  4 1 2 4 ---- ---- ---- ---- ---- 4 65 4 5 6 4 3  6  5 ---- ---- ---- 3 5 ---- ---- ---- 5 66 5 6 4 6 5  4  6 ---- ---- ---- 2 4 ---- ---- ---- 6 3. We are about to award 5th place but we are going to tabulate the next column on the worksheet which is “4th place and higher.”  Neither of the two remaining couples have a majority so we move to the “5th place and higher” column.  #65 has 5 “4th place and higher” marks and #66 has 4. #65 is, therefore, awarded 5th place and #66 6th place.       The important thing to remember here with Rule 6 is that more than one place can be awarded while working in one column of the work sheet. The placement being assigned may not coincide with the column/marks that you are working with. The second thing to remember is that all the couples assigned a place must have achieved a majority when they are assigned a position. Rule -7- If two or more couples have an equal majority for the same position. Now is the time to add together the place-marks and not just count them. There are seven judges so the majority is 4. 1. #71 is awarded 1st place by virtue of a majority of “1st place marks.”  We now move to the second column, looking for “2nd place and higher” (Rule 5), or even different majorities (Rule 6).  We find, however that there are two couples, #72 and #73, who have an equal majority of “2nd and higher” place marks.       WALTZ   Judges Places Result No A B C D E F G 1 1-2 1-3 1-4 1-5 1-6 1-7 1-8   71 3 1 6 1 1 2 1 4 ---- ---- ---- ---- ---- ---- ---- 1 72 2 2 1 5 3 1 3 2 4(6) ---- ---- ---- ---- ---- ---- 2 73 1 5 4 2 2 6 2 1 4(7) ---- ---- ---- ---- ---- ---- 3 74 5 4 2 4 6 5 4 ---- 1 1 4(14) 6 ---- ---- ---- 4 75 4 6 3 3 5 4 6 ---- ---- 2 4(14) 5 ---- ---- ---- 5 76 6 3 5 6 4 3 5 ---- ---- 2 3 5 ---- ---- ---- 6 2. Add (not count!) the place-marks for each couple that has the majority. Adding the four “second and higher” place marks for #72, (2+2+1+1) gives a total of 6.  Doing the same for #73 gives a total of 7.     3. The couple with the lowest total (sum) is awarded the position. Therefore, #72 is awarded 2nd place and #73 is awarded 3rd place.     4. This process continues until all couples with the equal majority have been awarded positions.  You then go back to the remaining couples in the section.  We continue with the “3rd place and higher” column to award 4th position, even though we are working in the “3rd and higher” column.     5. OK! Next question, “Same majority, same sum . . .?”  Hang in there for just a moment.       6. Continuing with the example.     7. Count the number of “3rd and higher.” None of the three remaining couples, #74, #85, and #76, have achieved a majority.  Moving on to the “4th and higher” column we find that #74 and #75 have an equal majority whereas #76 does not.     9. We now focus only on the two couples #74 and #75 who have an equal majority.  Adding the place marks together they both have an equal total (sum) of 14.  The problem is still not resolved.     10. As far as “4th place and higher” is concerned the two couples #74 and #75 are still tied.  We, therefore, move to the next column “5th and higher” to try and break the deadlock.  Counting the “5th and higher “ place marks we find that #74 has a majority of 6 and #75 a majority of 5.  #74 is awarded the 4th place by virtue of the larger majority, (effectively back to Rule 6) and #75 is awarded 5th position.     11. We now move back to the “5th and higher” column for #76.  Counting their “5th and higher” place marks gives a count of 5, a majority, and they are therefore awarded 6th place.     12. The third part of Rule 7 defines a tie.  There are situations where no matter how many rules you apply you cannot separate the couples.  In the event of two couples having an equal majority and also an equal sum, we go to the next column, FOR THESE COUPLES ONLY.  If the next column still gives us an equal majority and sum we go to the next column, and the next until we reach the last possible column.  For 6 couples this will be “6th and higher,” for 7 couples “7th and higher,” and for 8 couples “8th and higher.”  Remember that if you have more than 8 couples you will not be running a final! If we still have a tie at the last column then each couple is awarded the average or mean of the positions that we are working with.  If we have two couples and we are looking to place 3rd and 4th each couple will be awarded the 3½th position, (3 + 4 = 7 ¸ 2 = 3½).  For a 3-way tie for 3rd, 4th, and 5th positions, each couple is placed 4th, (3 + 4 + 5 = 12 ¸3 = 4). This describes the mathematical methodology that the scrutineer uses to calculate the results.  When the compere announces the results, they are all listed as the highest of the positions involved in the tie.  In the example above the first two couples are announced as being tied for 3rd place.  In the second, the three couples are tied for 3rd place. Rule 7 is as complicated as it gets when working with the individual dances.  Rule -8- If no couple receives a majority for the position under review. After Rule 7, Rule 8 is simplicity itself. If no couple achieves a majority of 1st place marks then you move on to the “2nd place and higher” column. If there is no majority there you continue onto the next column and the next until one or more couples achieve a majority. When one or more couples are found with a majority, subject to Rule 6 and Rule 7 the 1st place is awarded. We then continue in a similar manner to allocate all other positions. There are 7 judges so the majority is 4. 1. We are looking for 1st place marks. No couple has a majority. We move on to the “2nd and higher” column. No couple has a majority in that column either. Moving on to “3rd and higher” we find that couples #81 and #82 have a majority of 6 and 4 “3rd and higher” place marks each. Subject to Rule 6 we award 1st place to #81 and 2nd place to #82. WALTZ Judges Places Result No A B C D E F G 1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 81 3 3 3 2 5 2 3 ---- 2 6 ---- ---- ---- ---- ---- 1 82 4 4 4 3 2 3 2 ---- 2 4 ---- ---- ---- ---- ---- 2 83 2 2 6 6 4 1 4 1 3 3 5 ---- ---- ---- ---- 3 84 1 6 1 5 1 4 6 3 3 3 4 ---- ---- ---- ---- 4 85 4 5 5 1 3 6 1 2 2 3 3 6 ---- ---- ---- 5 86 5 1 2 4 6 5 5 1 2 2 3 5 ---- ---- ---- 6 2. We are now looking to award 3rd place. Tallying the “4th and higher” column we find that both couples #83 and #84 have a majority of “4th and higher” place marks. Again using Rule 6 3rd place is awarded to #83 and 4th place to #84. 3. We are now looking to award 5th place. Tallying the “5th place and higher” column both #85 and #86 have achieved a majority. Rule 6 places #85 in 5th position and #86 in 6th. 4. Remember the column that you are working with may not coincide with the position you are looking to award. So, with Rule 5, Rule 6, Rule 7, and Rule 8 you can work out the results for a single dance with simple majorities, multiple majorities, tied majorities, and no majorities! Rule -9- Compilation of the final summary. Final Summary No Dances Total Result W T V SF Q     91 1 1 1 1 1     5 1 92 4 2 2 2 2     12 2 93 2 3 3 3 3     14 3 94 5 5 6 4 5     25 4 95 3 4 5 7 7     26 5 96 6 7 4 5 6     28 6 97 7 6 7 6 4     30 7 98 8 8 8 8 8     40 8 We now move on to Rule 9, Rule 10, and Rule 11. These apply to multiple-dance sections as found in Ballroom and Latin competitions. It covers the whole gambit from the D-Beginners class containing three dances, Waltz, Tango and Quickstep or Cha-Cha-Cha, Rumba and Jive to the Championship sections of five dances and the combinations of six, eight, and ten dances. All of the results, and only the results not the individual place-marks, are transferred into a new table called the “Final Summary.” These results are then simply added together, not counted, to give a total. The couple with the lowest total is awarded 1st place in the section; the next highest total is awarded 2nd place, and so on until all couples have been placed. Final Summary No Dances Total Result S C R J       11 1 2 1 1       5 1 12 2 1 2 2       7 2 13 3 4 3 4       14 ? 14 4 3 4 3       14 ? 15 6 6 5 7       24 5 16 5 5 7 8       25 ? 17 7 7 6 5       25 ? 18 8 8 8 6       30 8 After having transferred the individual dance results to the “Final Summary” we see that #91 has the lowest total of 5 and is therefore awarded 1st place. #92 has the next lowest total and is awarded 2nd place. We continue in this way for all couples with #98 being placed 8th. In the event that two or more couples have an equal total for the position under review, then there is a tie for that place. We use Rule 10 and Rule 11 to break the tie for multiple-dance sections in the same way that as we did for the individual dances and a single dance section. #11 and #12 are placed 1st and 2nd, respectively. #13 and #14 both have the same total and cannot be placed, we need Rule 10 and Rule 11 to break the tie. They will be awarded 3rd and 4th places. #15 has the next lowest total and is placed 5th. #16 and #17 are tied and require Rule 10 and Rule 11 to break the tie for 6th place. With the largest total of 30, #18 is placed 8th. Rule -10- If there is a tie for a place in the Final Summary. Rule 10 is the most involved of all the Rules. There are several sections to Rule 10. Let’s try and be simple and take it one section at a time. Final Summary No Dances Total Result W T SF         101 1 1 3         5 1 102 2 2 1         5 2 103 6 4 2         12 3 104 5 3 4         12 4 105 4 5 5         14 5 106 3 6 6         15 6                                           One important point, before we start.  Whilst working within Rule 10 we are not looking for the majority of anything.  It is another case of the more the better! 1. There is a tie for 1st place under Rule 9 for the section.  You must now look, in the Final Summary, to see which of the tied couples has won the most 1st places (won most dances).  Couples #101 and #102 both have a total of 5.  However, #101 has achieved 2 1st places whilst #102 has only 1 (in the Final Summary).  #101 is therefore awarded overall 1st place and #102 overall 2nd place.      2. It is important to note that if more than two couples are tied for 1st place then after one of the couples has been awarded the overall 1st place the remaining couples are actually tied for 2nd place. You must therefore count “2nd and higher” places for the remaining couples to try and award the overall 2nd place.  If you have a tie, the couples all have the same number of places, then, as before, you add the places together to provide a total.  The couple with the lowest total is awarded the place and the remaining couple is awarded the next place.     3. Here the similarity, with the previous single-dance rules, ends.  If the two couples have the same number of places and the same total you do not go to the lower places to break the tie.  At this point the couples are tied under Rule 10 and you must apply Rule 11 to break the tie. #101, #102, #103, and #104 all have a total of 12 and therefore must be considered for 1st place. #101 has more 1st places (2) than the other and is therefore awarded the overall 1st place.  The remaining couples are now tied for 2nd place, so we must count “2nd and higher” places to award the position.  #102 has more “2nd and higher” places than the others and is therefore awarded the overall 2nd place, (even though the couple did achieve any 1st places).  We are now left with #103 and #104 to be considered for the overall 3rd place. We now count “3rd place and higher”.  #103 (3) has more than #104 (2) and is therefore awarded the overall 3rd place.  #104 being the only remaining couple in the Rule 10 is automatically placed overall 4th. Final Summary No Dances Total Result W T SF Q       101 1 6 4 1       12 1 102 6 2 2 2       12 2 103 2 1 6 3       12 3 104 3 4 1 4       12 4 105 5 3 5 5       18 5 106 4 5 3 6       18 6                                           Having placed the first 4 places we must now award 5th place.  #105 and #106 have the same total so we count “5th and higher” places for the two couples.  #105 has the most (4) and is awarded the overall 5th place.  #106 as the last in this Rule 10 is awarded 6th. It is important to notice that although we had four couples with the same total under the Rule 10 we only placed one couple at a time.  Rule 10 is repeatedly applied to place each couple.  Rule 10 for 1st place (count the 1st places), Rule 10 for second place (count “2nd and higher” places), Rule 10 for third place (count “3rd and higher” places), and Rule 10 yet again for 4th place (count “4th and higher” places). If you have a tie under Rule 10 and cannot award places then you apply Rule 11.  The actual process, however, is to temporarily leave those couples and places that you cannot award and continue with the remaining couples and positions under Rule 10.  You then go back to the tied couples and apply Rule 11.  This keeps the process structured and logical, believe me! In summary you will have a tie under Rule 10 and need Rule 11 if: When allocating the overall 1st place all the tied couples have the same number of 1st places for the individual dances or if none of them have any 1st places. For all the other positions if the couples have the same number of places for the position under review and the totals of those places is the same you have a tie.  You will also have a tie if none of the couples have any places that are the same or higher than the position under review; you are looking to place 3rd and none of the tied couples have any “3rd or higher” places in the Final Summary. A final and very important point to remember.  You need to know how to handle the positions in the Final Summary that include fractions such as 2½, and 3½.  When evaluating place marks in the Final Summary table a fraction is considered to be a place mark for the next highest whole number. 2½ is viewed as 3 and 3½ is viewed as 4.  We cannot leave this as simple as that.  If when you have considered the place marks and the couples in the tie have the same number of place marks then, as above, you must add the place marks together to give a total.  When you do this you include the fractions at face value! Let’s try another example to sort it all out. 1. #102 and #107 both have a total of 8.  #102 has the most 1st places and is awarded overall 1st place.  With only two in the tie #107 is awarded overall 2nd place.     Final Summary No Dances Total Result W T VW SF Q     101 7 6 5 6 5     29 R11 102 1 3 2 1 1     8 1 103 5 5 6 7 6     29 R11 104 6 7 7 5 7     32 7 105 4 4 3 3 3     17 3 106 3 2 4 4 4     17 4  107 2 1 2 2 2     8 2                     2. #105 and #106 have the next highest total of 17.  We are now trying to place overall 3rd place and must therefore count “3rd and higher” places.  #105 has 3 and #106 has 2.  #105 is therefore awarded overall 3rd place and #106, the only other couple in the tie, is awarded overall 4th place.     3. #101 and #103 both have the next highest total of 29.  We are trying to place 5th place and must therefore count “5th and higher” positions.  They are both tied with two “5th and higher” places.  We must now add them to get a total.  Both have the same total of 10.  These two couples are therefore tied under Rule 10 and need to go to Rule 11.  They will be awarded overall 5th and 6th places, but we will leave them for the moment.     4. We now move to 7th place.  On inspection we see that there is only #104 with the highest total of 32.  That couple is therefore awarded overall 7th place.     5. By now you probably have a headache and your eyes are rolling.  If you have made it this far pat yourself on the back have a drink and then come back for the home straight, Rule 11. Rule -11- When there is still a tie after Rule 9 and Rule 10. Rule 11 is fairly simple to apply. Effectively you take all of the place marks given to the tied couples and process them as if it was a single dance. So if you have two dances in the section, say the Waltz and Quickstep and seven judges, in a Rule 11 all 14 place marks will be treated as if it was one dance. There has to be a sting in the tail, with Rule 11 it is when more than two couples are tied under Rule 10 and move to Rule 11. Rule 11 is applied to all tied couples and the “best” couple is awarded the overall placing under review. The remaining couples in the tie then revert to Rule 10. If there is a tie under Rule 10 for the remaining couples we go forward again to Rule 11. After awarding the next overall position to the “best” couple this time around we revert back again to Rule 10 for the remaining tied couples. This procedure of Rule 10 followed by Rule 11 is repeated until all of the tied couples have been awarded an overall placing. It is important to note that as with Rule 10, Rule 11 only places one couple at a time. The only time when two overall places are awarded is if there are two couples in the tie or you are placing the last two couples in the tie. The answer to your question is Yes! You can still have a tie under Rule 11. At this point we, the scrutineers, throw in the towel; there is no Rule 12! You have an unbreakable tie. To get rid of the problem you pass it to the Chairman of Adjudicators to decide. Typically if the tie is for 1st place a dance-off takes place between the tied couples. For the minor places the couples are, typically, awarded the tied position. Having initially stated that Rule 11 is simple lets work through an example: 1. #111 is the outright winner as the only couple to acquire any 1st places. They are awarded the overall 1st place. 2. #115 has the next lowest total and is therefore awarded overall 2nd place. 3. #112 and #114 have the next lowest total and are tied for overall 3rd place. They both have one 3rd place, the position under review. WE do not go to lower positions to break the tie, so they are tied under Rule 10 and must go to Rule 11. All marks for both dances are considered to be for one dance. We are looking to place overall 3rd and start by counting the “3rd and higher” places. Both #112 and #114 have 7 “3rd and higher” places. We move to “4th and higher” to try and split the tie. #112 has 11 “4th and higher” places and #114 has 13. #114 has the most and is awarded the overall 3rd place with #112 being awarded the overall 4th place. (Whilst in Rule 11 we actually apply Rule 5 through Rule 8 to the marks for each tied couple.)   WALTZ   Judges Places Result No A B C D E F G 1 1-2 1-3 1-4 1-5 1-6 1-7 1-8   111 1 1 1 1 1 1  1  7 ---- ---- ---- ---- ---- ---- ---- 1 112 5 3 5 4 3  3  3 ---- ---- 4 ---- ---- ---- ---- ---- 3 113 4 5 4 5 5  5  4 ---- ---- ---- 3 7 ---- ---- ---- 5 114 3 4 3 3 4  4  5 ---- ---- 3 6 ---- ---- ---- ---- 4 115 2 2 2 2 2  2  2 ---- 7 ---- ---- ---- ---- ---- ---- 2     Quickstep   Judges Places Result No A B C D E F G 1 1-2 1-3 1-4 1-5 1-6 1-7 1-8   111 1 1 1 1 2 1  1  6 ---- ---- ---- ---- ---- ---- ---- 1 112 5 3 3 4 3  4  4 ---- ---- 3 6 ---- ---- ---- ---- 4 113 4 5 5 5 5  5  5 ---- ---- ---- ---- 7 ---- ---- ---- 5 114 3 4 4 3 4  3  3 ---- ---- 4 ---- ---- ---- ---- ---- 3 115 2 2 2 2 1  2  2 ---- 7 ---- ---- ---- ---- ---- ---- 2   Final Summary   Rule 11 NO Dances Tot Res No Places W Q               3 4          Res 111 1 1           2 1 112 7 11         4 112 3 4           7 4 114 7 13         3 113 5 5           10 5                 114 4 3           7 3                 115 2 2           4 2                 4. #113 has the next lowest total of 10 and is awarded overall 5th place. Right that’s it, plain and simple. That is the Skating System, used most Saturdays by “Yours Truly” and the other scrutineers. The following section includes a Final Example for you to try. Solution 1. There are five judges for the dances. The majority is therefore 3 Foxtrot 2. Count the number of 1st places for each couple. The total is in the “1st” column. There is no majority so move to the “2nd and higher” column. 3. #115 and #116 both have the same total of 3 “2nd and higher” marks, which is a majority. The sum of these 3 marks is also equal (4). To break the tie we must move to the “3rd and higher” column. 4. #115 and #116 still have the same tie as neither achieved any 3rd place marks from the judges. Counting the “4th and higher” column we find that #115 has 3 “4th and higher” marks and #116 has 5. Both of these are a majority. By virtue of the larger majority #116 is awarded 1st place and, being only a two-couple tie, #115 is awarded 2nd place. 5. We must now go back to the “3rd and higher” column for the remaining couples. #114 has a majority of 3 “3rd and higher” place marks and is given 3rd place. 6. Moving onto the “4th and higher” column for the remaining couples we find that none of them has a majority, so we move straight on to the “5th and higher” column. Note: Do not get confused by the marks for #115 and #116 in the “3rd and higher” and “4th and higher” columns. They are part of placing those two couples 1st and 2nd and are not included in any further inspections. 7. Counting “5th and higher” we find that #111 and #118 both have a majority of 3 “5th and higher” place marks. The sum of these 3 place marks is lower for #111 (11) than for #118 (12). As a result of the lower sum #111 is given 4th place and #118 gets 5th place. 8. We now inspect the “6th and higher” column for the remaining three couples. #112 has a majority of 3 place marks and is placed 6th. 9. In like manner #117 has a majority of 4 “7th and higher” place marks and is given 7th place. 10. #113 is the only couple left and is given 8th place. For correctness you should take the trouble to enter the place marks for #113 in the "8th and higher" column. The work sheet is then 100% correct and complete. 11. Finally copy the results into the “F” column in the Final Summary work sheet. Tango 12. A similar process is followed for the Tango. In summary: 13. #115 takes 1st place because of a lower sum of “2nd and higher” place marks. It is a two-couple tie with #116 who is automatically placed 2nd. 14. #114 takes 3rd place, having a sole majority of “4th and higher” place marks. 15. Likewise #118 is given 4th place with a sole majority of 3 “4th and higher” place marks. 16. A sole majority of “5th and higher” place marks gives #111 5th place. 17. Next is #113 in 6th place with a sole majority of “6th and higher” place marks. 18. When the “7th and higher” column is inspected, #117 has a greater majority (5) of “7th and higher” place marks than #112 (3). #117 is, therefore, placed 7th and #112 is placed 8th. 19. Copy the results into the “T” column in the Final Summary work sheet. Final Summary 20. Each couple’s positions are now added to give a total. In this example they are 9, 14, 14, 6, 3, 3, 14, 9 21. #115 and #116 both have the lowest total of 3 and are considered for 1st place. Each has won one 1st place and are, therefore, tied under Rule 10. We must use Rule 11 to break the tie. Leave them for the moment. These two couples will eventually take 1st and 2nd place 22. The next lowest total is #114 with 6. #114 can immediately be awarded 3rd place. 23. We must now allocate 4th place. #111 and #118 both have a total of 9 and the sums are equal at 9. They are also tied under Rule 10. Rule 11 here we come again, but leave it for a while! 24. We have three remaining couples, #112, #113, and #117 each with a total of 14. We are looking to allocate 6th place. #117 has not achieved any 6th places and therefore immediately drops out, being awarded 8th place. #112 and #113 have both achieved one 6th place and are therefore tied under Rule 10. A third visit to Rule 11 to break a tie. 25. Well here we are at last Rule 11: #115 and #116 for 1st and 2nd place #111 and #118 for 4th and 5th place #112 and #113 for 6th and 7th place Do not forget. We are now treating the two dances with five judges each as a single dance with ten judges. The majority whilst in Rule 11 is 6 26. We have to allocate 1st place. Inspecting the 1st place marks for #115 and #116 show a total of 4 and 2 respectively. There is no majority and 1st place cannot be awarded. We move to “2nd and higher” place marks. Both couples have a total of 6 “2nd and higher” place marks. They are still tied. Summing these 6 place marks gives a sum of 8 for #115 and 10 for #116. By virtue of the lower sum #115 is awarded 1st place and #116 is awarded 2nd place. 27. We must now consider #111 and #118 for 4th place. Inspecting the total of “4th and higher” place marks for each we find that #111 has a total of 4 place marks and #118 has a total of 5. Neither of these represents a majority. We now inspect the “5th and higher” place marks. #111 has a total of 7 “5th and higher” place marks and #118 has a total of 6. By virtue of the larger majority #111 is awarded 4th place and #118 gets 5th place. 28. We finally move to #112 and #113 to allocate 6th place. Inspecting “6th and higher” place marks for each, shows a total of 4 “6th and higher” place marks for #112 and 5 for #113. Yet again neither of these is a majority. Considering the “7th and higher” place marks, #112 has a total of 7 and #113 a total of 5. Both of these are a majority. The greater majority for #112 gets them 6th place and #113 gets 7th place. You’ve finished... CONGRATULATIONS!!!