This is my first question on the Math SE, and it may be a bit simple. Apologies if my question reveals my misunderstanding of your field or the universe in general. Me Programmer.
I am working on a maths game to teach kids the use of multiplication, division and logic. Kids are given a sum of a set, and the values in a set. They need to show that they can work out the numbers in the set by dividing the sum into smaller parts (dividing by 1-10) and adding the product of that division to other products of that division. They can only use whole numbers.
For a really simple example, with a set of 30, 30 and 40 (and a sum of 100), can be solved by:
100/10 (split 100 into ten parts) 10+10+10 (add three lots of 10, etc.) 10+10+10 10+10+10+10
With a set of 18, 18, 12, and 6 and a sum of 54:
54/2 = 18 with 18 left over r18 = 18 r18/3*2 = 12 with 6 left over r6 = 6
But I can't see a way to solve this with a Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 with the sum 376
Or a set of prime numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23 with the sum 100
Given the sum of a set of numbers, is there a relationship between the sum of the set and the numbers in the set (other than the obvious) that I can exploit to create problems for the kids to solve? Is there a way to test whether a set is solvable in this game, or a formula I should be using to test/generate the problems?