2 Groups
Alison and Sam: 10,30,50,70,90
Pattern: 10 x odd numbers
Even multiples of 5 (times 10) to numbers that aren’t multiples of 4
Sam and Matt: 30
Even numbers that are multiples of 3 but NOT 4 and 9
Alison and Matt: 15, 30, 60
Pattern: 5 x (times 2 of the number times to 5 before)
Multiples of 3 and 5 that aren’t multiples of 9(2 digits can’t add up to 9)
Alison and Becky: 10, 15, 45, 55
Triangular numbers that are multiples of 5(ending with either 5 or 0)
Becky and Sam: 66, 78
Even triangular numbers that aren’t multiples of 4
3 Groups
Alison and Sam and Matt: 30
Alison and Becky and Sam: 10
Becky and Sam and Matt: 66, 78
4 Groups
Alison and Becky and Sam and Matt:
If we list some of the larger multiples of 5: 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265,270, 275, 285, 290, 295, 300, 305, 310, 315, 320, 325…. I know from trial and error that the number won’t be in the 2 digits or the hundreds
If we pick of the triangular numbers from that list: 210, 325
If we then look for even numbers that aren’t multiples of 4: 210
And 210, is a multiple of 3 but not 9
.
. . The smallest number that is in all 4 of the groups is 210