# Fill the table so every consecutive 3 numbers sums to 50 or 100

Arrange numbers 1 to 40 to the table with rules:

• Multiple of 4 Numbers and some perfect square numbers are already there as guide.
• Every 3 consecutive numbers with pattern white-yellow-white, must sums to 50 or 100.
• There is only 1 unique solution.
• Some smart guessing are needed.

This is the sample for sums to 40 or 80.

• Do you mean that all multiples of 4 and all perfect squares are filled in, so none of the blanks will take those values? Nov 21 '17 at 4:07
• @jasen ok sory except 1. Nov 21 '17 at 4:16

## 1 Answer

My solution (I didn't verify uniqueness):

Here's generally how I solved it:

The first step was to place $6$, $13$, and $37$ (and then $38$). Then I looked at the square between $20$, $32$, and $36$. It must be odd, because otherwise one of the numbers above or below the $20$ would be a multiple of $4$. Checking every possibility doesn't actually take very long, and you can't go very far using any other number but $11$.

That gets you to

Then

I made a couple of informed guesses, using the information that the $3$ and the $5$ can't be in the same group, that the $40$ must be part of a group summing to $100$, and similar things. Wrong guesses quickly lead to contradictions at this point.