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A table of all possible number of waves under 50 is:
occasions waves sequence
0 0
1 1 1
2 3 1 1
1 6 6
3 6 1 1 1
2 8 1 6
4 10 1 1 1 1
3 11 1 1 6
2 13 6 1
4 15 1 1 1 6
5 15 1 1 1 1 1
3 16 1 6 1
2 18 6 6
4 20 1 1 6 1
5 20 1 1 1 1 6
3 21 6 1 1
3 21 1 6 6
6 21 1 1 1 1 1 1
4 25 1 1 6 6
4 25 1 6 1 1
5 25 1 1 1 6 1
3 26 6 1 6
6 26 1 1 1 1 1 6
7 28 1 1 1 1 1 1 1
4 30 6 1 1 1
4 30 1 6 1 6
5 30 1 1 6 1 1
5 30 1 1 1 6 6
3 31 6 6 1
6 31 1 1 1 1 6 1
7 33 1 1 1 1 1 1 6
4 35 6 1 1 6
4 35 1 6 6 1
5 35 1 6 1 1 1
5 35 1 1 6 1 6
3 36 6 6 6
6 36 1 1 1 6 1 1
6 36 1 1 1 1 6 6
8 36 1 1 1 1 1 1 1 1
7 38 1 1 1 1 1 6 1
4 40 1 6 6 6
4 40 6 1 6 1
5 40 6 1 1 1 1
5 40 1 6 1 1 6
5 40 1 1 6 6 1
6 41 1 1 1 6 1 6
6 41 1 1 6 1 1 1
8 41 1 1 1 1 1 1 1 6
7 43 1 1 1 1 1 6 6
7 43 1 1 1 1 6 1 1
4 45 6 6 1 1
4 45 6 1 6 6
5 45 6 1 1 1 6
5 45 1 6 1 6 1
5 45 1 1 6 6 6
9 45 1 1 1 1 1 1 1 1 1
6 46 1 6 1 1 1 1
6 46 1 1 6 1 1 6
6 46 1 1 1 6 6 1
8 46 1 1 1 1 1 1 6 1
7 48 1 1 1 1 6 1 6
7 48 1 1 1 6 1 1 1
Both 36 and 45 total waves have three possible numbers of occasions that would produce that total: in the case of 36: 3, 6 and 8; in the case of 45: 4, 5 and 9. But only in the latter case can one of the numbers of occasions be reached in three different ways: 5 occurrences.
So They waved the pompoms 5 times (the team scored 5 times), and the total number of waves was 45.
The above table was produced by sorting the output of this program, by waves major and occasions minor:
DECLARE SUB try ()
OPEN "aussie.txt" FOR OUTPUT AS #2
DIM SHARED h(10), num, tot, score
try
CLOSE
SUB try
IF tot < 50 THEN
FOR i = 1 TO num
PRINT #2, h(i);
NEXT
PRINT #2,
END IF
IF tot < 49 THEN
score = score + 1
tot = tot + score
h(num) = 1
try
tot = tot - score
score = score - 1
num = num - 1
END IF
IF tot < 44 THEN
score = score + 6
tot = tot + score
h(num) = 6
try
tot = tot - score
score = score - 6
num = num - 1
END IF
END SUB
Puzzle from Enigma No. 1424 by Richard England, New Scientist 6 January 2007.
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