Satisfying Statements-Solution
We start by finding as much 2 digit numbers as we can for each pair of statements so we are able to see a pattern. Lets say that Alison is A, Becky is B, Sam is S, and Matt is M. Here are the numbers that I found:
AB:
10, 15, 45, 55
AS:
10, 30, 50, 70, 90
AM:
15, 30, 60, 75
BS:
10, 66, 78
BM:
15, 21, 66, 78
SM:
30, 42, 66, 78
Now, we try to find 2 digit numbers in three of the statements.
ABS:
10
ABM:
15
ASM:
30
BSM:
66, 78
The smallest number in all 4 sets is:
ABSM:
210
The numbers that satisfy Alison and Sam’s statements are all multiples of ten with a odd number before the zero.
The numbers that satisfy Alison and Matt’s statements are all multiples of 15, except that 45 is missing because it is a multiple of 9.