Three girls at the school fair were each buying a raffle ticket.

The only unsold tickets were numbered 4,6,9,21 and 26.

After their three purchases were completed, their friend Tom noted that –

- The total of the three numbers was not a prime number.
- The total was not divisible by 17.
- Bernie did not have the largest number of the three
- Bernie did not have the smallest number of the three.
- One of their tickets was no 4
- The total of the three ticket numbers was not a square number
- Bernie’s ticket had an even number
- The number chosen by Carol would divide exactly into the product of the numbers chosen by Anne and Bernie

**Unfortunately, only THREE of Tom’s eight statements are true.**

What were the numbers of each of the girls’ tickets?

Posted by Ken.Kabaki
on Oct 1st, 2009 and filed under Discussions.
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we know that we have 4 .

Bernie : even number , not the big and not the small , so 4 and 26 eliminated (generally) , So Bernie’s nbr is 6.

we have then : 4 – 6.

finally , the sum is not prime , so 4-6-21 (31) and 4-6-9 (19) eliminated

then the solution is : 4 6 26

Yup. And the unique answer for 7/8 true statements would be

A=26

B=6

C=4

Anne Bernie Carol Sum (ABC) Not Prime Sum not divis by 17 B not max B not min one = 4 not Square B = even A*B/C True Count

9 21 6 36 TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE 3

6 21 4 31 FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE 4

9 21 4 34 TRUE FALSE FALSE TRUE TRUE TRUE FALSE FALSE 4

21 9 6 36 TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE 4

6 9 21 36 TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE 4

6 21 9 36 TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE 4

21 9 26 56 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE 4

26 9 21 56 TRUE TRUE TRUE FALSE FALSE TRUE FALSE FALSE 4

4 21 9 34 TRUE FALSE FALSE TRUE TRUE TRUE FALSE FALSE 4

9 6 21 36 TRUE TRUE TRUE FALSE FALSE FALSE TRUE FALSE 4

6 26 9 41 FALSE TRUE FALSE TRUE FALSE TRUE TRUE FALSE 4

6 26 21 53 FALSE TRUE FALSE TRUE FALSE TRUE TRUE FALSE 4

9 6 26 41 FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE 4

21 6 26 53 FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE 4

26 6 9 41 FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE 4

26 6 21 53 FALSE TRUE TRUE FALSE FALSE TRUE TRUE FALSE 4

6 9 26 41 FALSE TRUE TRUE TRUE FALSE TRUE FALSE FALSE 4

6 21 26 53 FALSE TRUE TRUE TRUE FALSE TRUE FALSE FALSE 4

6 9 4 19 FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE 4

4 26 21 51 TRUE FALSE FALSE TRUE TRUE TRUE TRUE FALSE 5

21 4 26 51 TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE 5

21 26 4 51 TRUE FALSE FALSE TRUE TRUE TRUE TRUE FALSE 5

26 4 21 51 TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE 5

6 4 26 36 TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE 5

9 4 21 34 TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE 5

21 4 9 34 TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE 5

26 4 6 36 TRUE TRUE TRUE FALSE TRUE FALSE TRUE FALSE 5

9 26 21 56 TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE 5

21 6 9 36 TRUE TRUE TRUE FALSE FALSE FALSE TRUE TRUE 5

21 26 9 56 TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE 5

21 9 4 34 TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE 5

26 21 4 51 TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE 5

4 9 21 34 TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE 5

4 21 26 51 TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE 5

26 21 9 56 TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE 5

9 21 26 56 TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE 5

6 4 21 31 FALSE TRUE TRUE FALSE TRUE TRUE TRUE FALSE 5

4 21 6 31 FALSE TRUE FALSE TRUE TRUE TRUE FALSE TRUE 5

4 26 6 36 TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE 5

9 26 6 41 FALSE TRUE FALSE TRUE FALSE TRUE TRUE TRUE 5

21 26 6 53 FALSE TRUE FALSE TRUE FALSE TRUE TRUE TRUE 5

4 9 6 19 FALSE TRUE FALSE TRUE TRUE TRUE FALSE TRUE 5

26 9 6 41 FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE 5

26 21 6 53 FALSE TRUE TRUE TRUE FALSE TRUE FALSE TRUE 5

6 4 9 19 FALSE TRUE TRUE FALSE TRUE TRUE TRUE FALSE 5

4 6 26 36 TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE 6

4 26 9 39 TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE 6

26 4 9 39 TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE 6

26 9 4 39 TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE 6

4 9 26 39 TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE 6

21 6 4 31 FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE 6

4 6 21 31 FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE 6

21 4 6 31 FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE 6

6 26 4 36 TRUE TRUE FALSE TRUE TRUE FALSE TRUE TRUE 6

9 4 26 39 TRUE TRUE TRUE FALSE TRUE TRUE TRUE FALSE 6

9 26 4 39 TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE 6

9 6 4 19 FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE 6

4 6 9 19 FALSE TRUE TRUE TRUE TRUE TRUE TRUE FALSE 6

9 4 6 19 FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE 6

26 6 4 36 TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE 7

Annie has 9

Bernie has 21

Carol has 6

Statements 1, 2, and 4 are TRUE

The sum (36) is not prime, is not divisible by 17, and Bernie does not have the smallest number of the three

Statements 3, 5, 6, 7, 8 are all FALSE

Bernie DOES have the largest number (21 vs 9 and 6)

NONE of the tickets was a ‘4’

The total WAS a square number (36)

Bernie’s ticket was NOT even (21)

Carols number (6) does NOT divide into 9*21 = 189

I believe this is the only solution. Process for solution involved creating ‘truth matrices’ where i checked each of the statements against the 60 possible combinations of numbers (the order of the numbers matters). Then I found where the sum of True Statements was 3.