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?