Number Pyramid
Fill in a number pyramid where every block is the sum of the two blocks below it.
A number pyramid stacks blocks so that each block holds the sum of the two blocks directly below it. The bottom row is the widest and every row above it has one block fewer. Fill in the blocks you know, leave the rest blank, and the solver works out the whole pyramid.
Separate numbers with spaces or commas. Use ? (or _ or x)
for a blank block. Each row must have exactly one block more than the row above it.
Bold blocks with a tinted background are the numbers you supplied. The rest were computed.
How it works
Every block equals the sum of the two blocks beneath it, which gives three handy rules. If you know the two children, the parent is their sum. If you know the parent and one child, the other child is the parent minus the known child. The solver applies these rules over and over until no new block can be filled.
When simple rules leave gaps, the solver switches to algebra. Each block can be written as a weighted sum of the bottom row, where the weights are the entries of Pascal's triangle. Every block you supplied becomes one equation in the unknown bottom blocks, and the solver clears the system with Gaussian elimination, then rebuilds the pyramid from the bottom up.
If there are too few clues to pin down a single answer, the solver says so. If the numbers you gave cannot all be true at once, it reports a conflict instead of guessing.