Fun Maths Problem

[Felix-The-Ghost]

Bonus marks if you can find a simple method to find the actual consecutive numbers.

I guess we didn't explicitly do this:

Say you want to find a sequence of x consecutive numbers that total up to y.

If x is an odd number, y must be divisible by x for there to be a possible solution for x numbers.

e.g. find out which 3 numbers can make 21.

21/3 = 7 -- then you add an equal amount of numbers on both sides of this number until you have a sequence of x numbers and there's your answer.

6...7...8 (6+7+8=21)

If x is even, it's a little different. The quotient of y/x must be exactly between two integers. You can double y temporarily and half the quotient to see if it is between two integers (basically 2y/x must be an odd number)

e.g. find out which 4 numbers can make 14.

14/4 = 3.5 OR 14*2(28) / 4 (7) / 2 (3.5)

The middle numbers of your sequence will be Q - 0.5, Q + 0.5, where Q is the quotient to the above problem (when it is exactly between two integers)

3...4

Add numbers to both sides until you have a sequence of x numbers:

2...3...4...5 (2+3+4+5=14)