Guess my number: the higher-or-lower game for children

"Is it 7?" "Lower." "Is it 3?" "Higher!" "So it's 4, 5 or 6…"

The higher-or-lower game needs nothing at all: one person thinks of a number, the other guesses, and the only clues are "higher" and "lower". It works in the car, in a queue or at bedtime. It practises number order, comparing numbers and the idea of "between", and with time children discover a real strategy hidden inside it.

How to play

One player thinks of a number in a range everyone agrees on, for example 1 to 10.
The other player guesses a number.
The first player answers "higher", "lower" or "that's it!"
Count the guesses. Then swap roles.

With a younger child, write the secret number on a piece of paper and turn it over before you start. Then nobody can change their mind halfway, and at the end the paper proves the answers were honest.

A number line on paper

Write the numbers in a row: 1, 2, 3 … 10. Each time you hear "higher" or "lower", cross out the numbers that can't be the answer.

Guess	Answer	What's left
7	Lower	1 to 6
3	Higher	4, 5, 6
5	Higher	6

Seeing the crossed-out numbers helps young children understand what "higher" means: not "a bit higher", but "anywhere above that number". It also makes the next question clear: which numbers are still possible?

The clever strategy: guess the middle

At first, most children guess at random or go up one at a time: 1, 2, 3, 4… After a few games, ask: "Which guess gets rid of the most numbers?"

If the number is between 1 and 10, guessing 5 rules out about half of them, whatever the answer. Guessing 1 rules out only one number if the answer is "higher". Always guessing the middle of what's left means you'll never need more than:

Range	Guesses needed at most
1 to 10	4
1 to 20	5
1 to 100	7

Children around eight and older are often amazed that seven guesses are always enough for 100 numbers. Try it: have them pick a number from 1 to 100, and guess the middle each time out loud so they can follow your thinking. Then let them try.

Finding the middle is good maths practice in itself. "What's halfway between 50 and 100?" "Between 51 and 60?"

Variations for different ages

Smaller numbers with fingers. For four- and five-year-olds, use 1 to 5 and let them show their guess on their fingers.
Bigger ranges. 1 to 20, then 1 to 100, then 1 to 1000 for older children who like a challenge (ten guesses are enough).
Pages in a book. Open a book at a secret page; your child guesses the page number.
Things on a ruler. Pick a secret mark on a ruler or a measuring tape: practice reading measurements too.
Count the guesses. Each player keeps a tally. Lowest total after three rounds wins.

Rough age	What to try
4–5	1 to 5 or 1 to 10; the secret number on paper; a number line with crossings-out
6–7	1 to 20; counting the guesses; taking turns choosing the number
8–9	1 to 100; discovering "guess the middle"; working out halfway points
10 and up	1 to 1000; explaining why the middle works; predicting how many guesses you'll need

Ages are only a rough guide, and every child is different.

In Dologi, the Math topic has "Put in order" puzzles, where children arrange things from smallest to largest. Knowing where each one goes in the order is the same skill the higher-or-lower game relies on.

In short

One person thinks of a number, the other guesses, and the only clues are "higher" and "lower".
A paper number line with crossed-out numbers makes the clues visible for young children.
Guessing the middle rules out half the numbers each time: 7 guesses are always enough for 1 to 100.
Change the range, the age and the setting: fingers, book pages, rulers.