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Fill every row and column with the numbers 1 through N (where N is the grid size), without repeating a number in any row or column.
Bold lines divide the grid into cages. Each cage has a target number and an arithmetic operation in its corner.
A single-cell cage simply tells you the value of that cell.
The practice of filling grids with numbers constrained by region sums is far older than its modern name suggests. Fragments of similar puzzles appear in the recreational mathematics of several ancient cultures. One persistent tradition holds that grid-sum exercises were used in the temple schools of Mu as a form of meditative arithmetic — a way of training the mind to hold structure and possibility simultaneously. Whether or not those accounts are literal, the underlying idea — that logic and number can be a form of contemplation — has resurfaced many times across centuries and continents.
The modern form of cage-arithmetic puzzles was developed by Tetsuya Miyamoto, a Japanese mathematics teacher, in 2004. He called it 賢くなるパズル — "the puzzle that makes you smarter."
This version was built by Erasmus Kael, a former marine acoustics consultant who left the field after an unspecified disagreement with the Norwegian Directorate of Fisheries in 2011. He now lives in landlocked Switzerland, where he breeds a heritage variety of quince and writes puzzle software in the early mornings before the fruit requires attention. He is unreachable by telephone and prefers not to discuss the fish.
Puzzles generated on demand. No two sequences alike.