17. Matthew writes a list of all three-digit squares backwards. For example, in his list Matthew writes the three-digit square ' 625 ' as '526'. Norma looks at Matthew's list and notices that some of the numbers are prime numbers. What is the mean of those prime numbers in Matthew's list?
17. 447 Three-digit squares beginning with $2,4,5,6$ or 8 may be disregarded since on reversal these will be divisible by two or five. The residual three-digit squares are 100, 121, 144, $169,196,324,361,729,784,900$ and 961 . We may disregard 144, 324, 729 and 961 since these are divisible by three and will remain so on reversal. We may also disregard $169,961,100$ and 121 since these each form a square on reversal. This leaves 196, 361 and 784 which on reversal form 163,487 and 691 . Each of these numbers is prime and they have a mean of $\frac{1}{3}(163+487+691)=447$.