How to Choose Logic Puzzles for Elementary School Kids

Japan’s national curriculum for elementary school mathematics lists, among its aims, the ability to see everyday situations mathematically and “think them through logically, with foresight” (my translation; MEXT, Course of Study for Elementary Schools, 2017, in Japanese). Many parents look for logic puzzles as a way to practise exactly that kind of step-by-step thinking.

The trouble is that bookshop shelves and app stores are full of things labelled “brain training” or “critical thinking”. This post lists what I would look at when choosing a logic puzzle for a child in elementary school, in the order I think matters most.

What counts as a logic puzzle

Here I mean a puzzle with fixed rules, where following reasons from the rules leads to the answer. Sudoku, mazes, the Tower of Hanoi, and “one of these three is lying” riddles are all examples.

They are different from trivia quizzes. A child does not need to know spellings or capital cities. The rules and the puzzle in front of them are enough. I think that is the real strength of logic puzzles.

What to look for

1. Can the child state the rules in their own words?

This comes first. When the rules are long, a child gets tired memorising them before any thinking starts. The rules of sudoku fit in one line: 1 to 9 once in every row, column and box.

In a shop, I would hand the rules to the child and ask, “How do you win?” If they can answer, the puzzle has passed the front door.

2. Is the answer decided by reasons, not by guessing?

A well-made logic puzzle has exactly one answer, and you can reach it by reasoning. A puzzle that you eventually solve by trying everything rewards moving your hands over using your head.

A simple test: after the child finishes, ask “Why does it go there?” If they can give a reason, the puzzle is training thinking. If they solved it without being able to say why, it is closer to a trial-and-error puzzle. That is not bad, but the purpose is a little different.

3. Are there plenty of easy puzzles, with small steps between levels?

Plenty of puzzle books are already hard by puzzle three. I believe a child’s first experience should be solving the first puzzle.

Look for something with lots of easy puzzles at the start and new ideas added a little at a time. Checking that the difficulty levels are finely graded saves a lot of frustration.

4. Can the child spot their own mistakes?

If checking always needs an adult, the child spends time waiting for the adult. When the rules themselves do the checking (in sudoku, two 5s in one row means something is wrong), the child can notice and fix the mistake alone.

5. Does one puzzle finish in a short time?

For elementary school children, puzzles that end in a few minutes to about 15 minutes are easier to keep up. Long puzzles lose focus halfway, and if they run into the next day, the child forgets where their thinking had got to.

6. Does it lean too hard on arithmetic or reading?

Some number puzzles, like sudoku, involve no calculation at all. Others are built around calculation. The second kind is useful as arithmetic practice, but a child who struggles with arithmetic will trip on the sums before reaching the thinking. It helps to know which kind you are buying.

Paper, physical puzzles and apps

Paper puzzles keep a record. You can sit down with the child afterwards and see where their thinking stopped. Erasing takes effort, which also encourages thinking before writing.

Physical puzzles such as the Tower of Hanoi show the result of each move directly. You move discs of different sizes to another peg, never placing a larger disc on a smaller one. With n discs, the fewest moves needed is 2 to the power of n, minus 1 (Wikipedia: Tower of Hanoi). Three discs take 7 moves. Once a child starts asking “what is the fewest moves?”, play slowly turns into logic.

Apps offer a lot of puzzles and instant feedback. On the other hand, when undoing is too easy, trying things quickly beats thinking. Ads and screen time are also things to weigh that paper does not raise.

I do not think you have to choose one. Practising reasons on paper and getting volume from an app is a reasonable mix.

When a puzzle is too hard

It happens often. Here is what I would do.

• Go back one level. An earlier puzzle in the same book or app is fine. Going back is not losing.
• Point to where to look, not to the answer. Instead of “what goes here?”, something like “have another look at this row”.
• Ask the child to think out loud. The adult only listens. Children often find their own mistake while explaining.
• Try again tomorrow. After a night’s sleep, a path that was invisible yesterday sometimes appears.

What I would avoid is solving it for them. Once the answer is known, that puzzle can no longer be used for thinking practice.

Where Math Gates fits

Math Gates is a circuit puzzle game I make. You place gates that change a number and mirrors that turn its path 90 degrees on the empty cells of a board, then press Run. A bit carrying a number travels in a straight line. The port at the end accepts only values that meet its condition.

Measured against the list above, this is what it is like. There are only three actions: tap a cell, choose a piece, run. When you place a piece, the result is drawn on the board as a dotted line, so you can check your prediction before running. When a run fails, it stops for a reason you can see: the bit hit a wall, a gate rejected its value, or the port’s condition was not met. There is no time limit and no lives. Stars depend on how many gates you used, and solving with the fewest gives three stars.

The seven worlds start with addition and subtraction, then move through multiplication and division, remainders, negative numbers, fractions, squares and square roots, and finally true, false and logic. Clearing 12 of the 20 puzzles in a world opens the next one.

On point 6, Math Gates is the kind of puzzle that does use arithmetic. It is aimed at ages 8 and up. If arithmetic itself is still shaky, a puzzle without calculation such as sudoku may be a better start. I covered the rules in Sudoku Rules: What First-Timers Need to Know.

It runs on iPhone and iPad. It is free to play with ads between puzzles, and a one-time purchase removes the ads. A Hint places one correct piece after you watch an ad, and that piece cannot be moved.

For what puzzles can and cannot teach, see What Is Computational Thinking, and What Can Puzzles Teach?. For who the game suits, see Who Is Math Gates For?.

A good logic puzzle, in my view, has short rules, answers with reasons, and a first puzzle the child can solve. If those three are there, the rest can be left to the child’s taste.