Flexi Cages takes the classic cage puzzle — fill a grid so every row and column has each number once, and every outlined cage makes its target with its operation — and lets you choose the numbers. The grid can use 1 to N as usual, but also 0 to N−1, multiples of ten, consecutive even or odd numbers, primes, negative numbers, unit fractions like ½ and ⅓, decimals, or letters.
Changing the numbers changes the thinking. With fractions, a + cage of 1⅚ means ½ + ⅓ + 1. With negatives, a + cage can make 0. With letters, the cage x²y tells you it holds two x’s and a y — algebra without any equations. Arithmetic is exact, so fractions stay fractions.
The idea comes from classroom work showing that one cage layout can teach many kinds of number sense — a “low floor, high ceiling” puzzle for every learner. Every puzzle here has exactly one answer and can be solved by reasoning alone.
Fill the grid so each row and column uses every number of the set once, and every cage makes its target with its operation.
The full guide, with a worked example and common mistakes: How to play Flexi Cages.
1 to N, 0 to N−1, tens, consecutive evens, consecutive odds, primes, negatives (centred on 0), unit fractions (1, ½, ⅓…), decimals, and letters x, y, z, w, v, u.
A cage like 2x + y or x²y tells you which letters are in it and how many of each. Rows and columns still use every letter once.
Yes — every puzzle is checked so that one answer fits, and it can be reached by reasoning.
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