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Loading ...The Raffle Tickets Brain Teaser
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?
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Posted by Ken.Kabaki
on Oct 1st, 2009 and filed under Discussions.
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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.