Grouping Goodies

Pat has 17 sweets in her bag. Rebecca found the next solution by taking groups of five sweets away at a time - number 12 doesn't work. Why doesn't 12 work?

Alistair from Histon and Impington Infants School said:

We know that the number of sweets is odd, because she has one left over when she counts in twos but 7 does. She could have 7 sweets or she could have 17 sweets, but she can't have 12 because it is an even number. There are no other numbers under 20 that fit these rules.