Can you find four consecutive numbers which add up to 10?, 14?, 50?, 106? Is there a quick way to find them?

Question

Given below is a figure. You have to fill in the numbers from 1 up to 16 in such a way that you get 29 when you add the numbers in each row.

Answer 1

I would divide the number by 4, and then subtract 1.5 and.5 for the first two numbers, then adding .5 and 1.5 for the third and fourth numbers.

Answer 2

Let n be the first number. Then the next number is n+1. Then n+2 and n+3. So:
n+n+1+n+2+n+3=x
4n+6=x
So, if x is 10, then n is 1. If you're using x,y then y=4x+6. So, 50=4x+6; 44=4x, x=11, and the four numbers are 11,12,13,14. Etc......
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