How to solve number pyramids, wheels and magic squares
Pyramids, wheels, magic squares: find the anchor
Structured number puzzles obey one local law everywhere. Find the cell whose neighbors are known, solve it, and let the structure fill itself.
Updated
Number pyramids, magic squares, and number wheels each impose one law repeated across the whole structure: every brick is the sum of the two below it; every line adds to the same constant; every spoke or opposite pair agrees. You never solve the whole structure — you solve one cell, and the law hands you the next.
Pyramids: sums go up, differences come down
A brick equals the sum of the two beneath it — so a missing lower brick equals the brick above minus its known partner. Chains of known bricks let you traverse: up by adding, down by subtracting. The query cell is rarely where you should start.
Magic squares: the constant first
Before touching the blank, compute the magic constant from any complete row, column, or diagonal. Every line — including both diagonals — must hit it. The blank sits on up to four lines; any one line with two known cells solves it, and the others verify it.
Wheels: opposite pairs and spoke sums
Number wheels hide their law in the geometry: opposite sectors summing to a constant, each spoke's outer−inner difference fixed, or steps around the rim. Test the candidate laws on the complete sectors first; the law that survives all of them is the rule.
The strategy
- Name the structure's law (and compute its constant) from fully known parts only.
- Find the anchor: the unknown cell with enough known neighbors to be forced.
- Propagate cell by cell toward the query.
- Verify the finished region against one untouched line of the structure.
Common traps
- Starting at the query cell and staring — anchors first.
- Magic squares: forgetting the diagonals also carry the constant.
- Pyramids: subtracting the wrong way when descending.
- Wheels: adopting the first law that fits one sector — it must fit every complete sector.
Speed · ~60s/item: Law → anchor → cascade is linear and calm: most structures fall in 45–75 seconds.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
Each brick is the sum of the two bricks directly below it. What number fills the empty brick?
Reveal the answer
The answer is A — 16.
Show why — the worked reasoning
Each brick is the sum of the two bricks directly below it. What number fills the empty brick?
Reveal the answer
The answer is E — 21.
Show why — the worked reasoning
Each brick is the sum of the two bricks directly below it. What number fills the empty brick?
Reveal the answer
The answer is E — 27.
Show why — the worked reasoning
Each brick is the sum of the two bricks directly below it. What number fills the empty brick?
Reveal the answer
The answer is C — 10.
Show why — the worked reasoning
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Questions people ask
Will pyramids, wheels and magic squares questions be on the free test?
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