# Is Sumplete always analytically solvable?

I am stuck here at Sumplete. I have tried looking for numbers that must be used/must not be used using https://combinationsumcalculator.com/ and all of them are either not used in all combinations (when I try to achieve a value by adding) or used at least in one combination when I sum the whole row/column and try to subtract to reach the target value.

Some of my techniques so far:

• if the target value is low (e.g. 4, you can exclude all higher values).
• if you need something like 8 and you have 3, 4, 5 and 6 you can exclude 4 and 6 because they can never be combined with something that results in 8.
• exclude single odd values. If the target is 12 and you are sure about 6 (e.g, 2 + 4 or 6 alone) and one of the values you have is 3 and that is the only odd value, you can exclude that because you can never combine that with something that results in an even value

The goal of this game is to pick the numbers that add up to the target number outside of the grid.

Trivia: it is ChatGPT who "developed" this puzzle game, although it is more or less a copy of one or several existing games.

• When it was initially released I tried it a few times, and it occasionally gave problems that had multiple solutions. Despite what ChatGPT claimed, it did not correctly check for that. I don't know if this has been fixed by now, but obviously on such a grid there is no way to deduce a solution. Jun 5 at 6:57

It depends on how much backtracking you still consider as analytically solvable.

For example, the first row here only has two options: 2+8 or 6+4.

Considering the case 2+8, now the third column only has two options, either take 8+1+1+6 or 5+5+6, either way 6 is selected.

This disables 9 in the last row, which in turn forces 5+4 in the 6th column, disabling the other 5 in the 4th row, forcing 8+1+1 on the third column.

From the initial 2+8 assumption in the first row, it forces 4 on the 4th column, disabling 3 in the last row, forcing 5 in the last row, forcing 3 in the last column, forcing 2 in the 7th row, forcing 1+1 in the first column.

Now second row has forces 1+8, while it should sum to 8.

Therefore our initial assumption of 2+8 in the first row is incorrect, and it should be 6+4. Then we can continue (e.g., disabling 4 in last column, which forces 1 in 5th row, etc.).