The Raffle Tickets Brain Teaser

ByKen.Kabaki

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 –

  1. The total of the three numbers was not a prime number.
  2. The total was not divisible by 17.
  3. Bernie did not have the largest number of the three
  4. Bernie did not have the smallest number of the three.
  5. One of their tickets was no 4
  6. The total of the three ticket numbers was not a square number
  7. Bernie’s ticket had an even number
  8. 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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    3 Comments

    1. 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

    2. 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

    3. 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.

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