1. The ages of Ramona's father, brother, and son are all prime numbers. In five years from now, their ages will all be perfect squares. What is the present age of each of them?
2. Find the digits a and b such that the six-digit number 543ab2 is divisible by 42. (Do not use a calculator for this problem, and be sure to explain how you found your solution.)
3. Five boxes have different weights, each less than 100 lb. When the boxes are weighed in pairs, the weights (in lbs) of all possible combinations are:
113, 116, 110, 117, 112, 118, 114, 121, 120, 115
What is the weight of the heaviest box?
4. Let N be a three-digit number whose digits are all distinct. There are nine two-digit numbers that can be formed using the digits of N. Assume that N is the sum of all nine of these two-digit numbers. Find all possible values of N.
5. The entries in the 3 x 3 array are all the digits from 1 to 9, arranged so that the entries in every row and every column are in increasing order. Given that the middle cell contains the number 5, how many such arrays are there?