Maths Challenges and Logic Puzzles

How many squares are there on a chessboard? If you said 64, think again, because there are a lot more than that. This is one of 45 puzzles in this free collection: some classics, many you will not find anywhere else, every one with an animated video solution.

No algebra. No formulas to memorise. Every puzzle is accessible enough for anyone to have a go at, and still a satisfying challenge if you have been solving problems for years. Good on your own, better with friends or as a family.

Every set of problems comes with a worksheet

All nine sets have a printable worksheet with the five puzzles laid out, ready to print out and work through away from a screen. They are included free when you sign in, along with all 45 animated video solutions.

1. Logic Puzzles

Five puzzles where the only tool you need is careful reasoning. Work out how many people are telling the truth, decide which cards you have to turn over to test whether a statement is true, and find which envelope holds the £20 note when only one of the clues is true. The set finishes with four players who all know there are exactly two blue hats and two red ones. Can they be sure of winning the game?

2. Counting Shapes

Counting sounds easy until the shapes start overlapping. Count the triangles hidden in a diagram, then the squares, then find out how many squares there really are on a chessboard. It is not 64. You will also hunt for octagons, and work out how many blue triangles appear in the sixth shape of a growing sequence without drawing it.

3. Magic Squares and Number Puzzles

Place the digits 1 to 9 exactly once so that every line adds to the same total, then work out which number is forced into the red circle. Two of these ask you to complete a magic square from scratch, and one hands you a finished square with two numbers secretly swapped and asks you to find them.

4. Area Puzzles

Five geometry puzzles with barely a formula between them. Find the area of a rectangle from three squares arranged around it, work out an area and then a value of x using only whole numbers, and compare a red region with a yellow one to find the difference between them without ever working out either area on its own.

5. Counting Puzzles

The systematic counting behind combinatorics, introduced through codes and numbers. How many three-digit codes are there? How many four-digit codes with no repeated digit? How many three-digit numbers whose last digit is the sum of the first two? The set ends with necklaces made from two blue beads and three red ones.

6. Primes and Factors

Five puzzles about the building blocks of numbers. Spot which number in a set is prime, find the missing digits in two different puzzles, and work out how many toppings, flavours and cones there are when all you know is that there are more toppings than flavours and more flavours than cones. Then crack a password.

7. Counting Routes

How many different ways are there to get from A to B? In the first three you may only travel left to right and never turn back. The fourth adds arrows that fix which way you can go. The last scatters coins across the grid and asks for the greatest number you can collect on a single journey right and down.

8. Chessboard Tiling

Five deceptively simple yes-or-no questions. Can you cover an 8×8 chessboard with two opposite corners removed using 2×1 tiles? What about 3×1 tiles, or L-shaped ones? What changes if only one corner is missing? And can 4×1 tiles cover a full 10×10 board? The answers are rarely the ones people guess.

9. Logic Puzzles 2

The hardest reasoning in the collection. Find the smallest number of moves needed to assemble a 100-piece jigsaw, then get two children and six adults across a river in a boat that carries only one adult or two children. Two coin-weighing puzzles follow: find the single light fake among seven coins, then find the forged stack among five stacks of five.