How to play Number Pyramid
The rules
The pyramid has a row of one cell at the top, and each row below has one cell more. Every cell above the bottom row is the sum of the two cells directly below it.
Some cells are given. Fill every other cell with a whole number so that all the sums are right. The numbers in the bottom row are from 1 to 9; the cells higher up can be much larger, up to three digits.
Every puzzle has exactly one solution, and logic alone is enough to reach it. You never have to guess.
How to play here
- Select a cell: click it, or use the arrow keys. Left and right move along the row; up and down move to the nearest cell in the row above or below.
- Enter a number: type its digits, or use the number pad below the pyramid. The first digit replaces what is in the cell; the next digits are added to the end (up to three digits).
- Erase: Backspace removes the last digit; Delete or the Erase button clears the cell.
- Undo and redo: Ctrl+Z and Ctrl+Y (on a Mac: ⌘Z and ⌘⇧Z).
- Hint: each press of Hint tells you more: first where to look, then which technique works there, and finally the number itself. If there is a mistake on the board, the hint shows you where.
When a cell and the two cells below it are all filled and the sum is wrong, the three cells are marked with stripes and a wavy underline.
Difficulty levels
The level is set by the hardest technique the puzzle requires:
| Level | Rows | Techniques required |
|---|---|---|
| Easy | 5 | Add and subtract |
| Medium | 5 | + Small triangles |
| Hard | 6 | + Big triangles |
| Expert | 7 | + Combining triangles |
Techniques
Add
Both cells below an empty cell are known: the empty cell is their sum.
Subtract
A cell and one of the two cells below it are known: the other cell below is the difference.
Small triangle
Go two rows down. The top cell equals the left cell plus two times the middle cell plus the right cell of that row (weights 1, 2, 1). If only one of these four cells is missing, you can work it out.
Big triangle
The same idea over more rows. Three rows down the weights are 1, 3, 3, 1; four rows down they are 1, 4, 6, 4, 1. If only one cell of such a triangle (its top or one of its bottom cells) is missing, you can work it out.
Combining triangles
Sometimes every triangle has two or more missing cells. Combine the highlighted triangles (add or subtract their equations, two or more of them) so that the other missing bottom cells drop out, and one bottom cell follows.
Tips
- Start with plain addition and subtraction: they often fill half the pyramid.
- Look for a known cell with known cells two or three rows below it: the weighted sums give you a missing cell straight away.
- Remember that every bottom number is between 1 and 9. It is a quick check on your arithmetic.
FAQ
- How does a Number Pyramid work?
- Each cell is the sum of the two cells directly below it. A few cells are given; you work out the rest by adding and subtracting. The numbers in the bottom row are from 1 to 9.
- Is there a new puzzle every day?
- Yes. A new Number Pyramid is published every day at each of the four levels: easy, medium, hard and expert. Earlier puzzles are in the archive.
- Do I need an account to play?
- No. You play right in your browser, with no sign-up and no cookies. Your progress is saved in your browser.