Numbers and arithmetic

Number Brain Teasers With Answers

Puzzles involving arithmetic, number sense and mathematical reasoning. Each challenge has two optional hints and a full explanation.

Set out what is known and what must be found. A small table, equation or careful count can make a tricky-looking number puzzle straightforward.

How it works: Read the problem, open a hint only if you need one, then reveal the answer when you're ready.

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10 challenges

NumbersEasy

Five consecutive numbers

Five consecutive whole numbers add up to 65. What are the numbers?

First hint

The middle number is the average.

Second hint

Divide 65 by 5.

Reveal answer and explanation

11, 12, 13, 14 and 15

The average is 13; the two numbers before and after 13 are 11, 12, 14 and 15.

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NumbersMedium

Coins in a pocket

A pocket contains eight coins, each worth either 2p or 5p. Their total value is 28p. How many of each coin are there?

First hint

Pretend all eight coins are worth 2p.

Second hint

Each 5p coin increases the total by 3p.

Reveal answer and explanation

Four 2p coins and four 5p coins

Eight 2p coins would be 16p. The extra 12p means four coins must be 5p; the remaining four are 2p.

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NumbersMedium

Hands of the clock

What is the smaller angle between the hands of a clock at exactly 2:20?

First hint

The minute hand moves 6° each minute.

Second hint

The hour hand moves 0.5° each minute.

Reveal answer and explanation

50 degrees

At 2:20, the minute hand is at 120° from twelve and the hour hand at 70° (60° + 10°). The difference is 50°.

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NumbersEasy

Two-digit mystery

A two-digit number has digits that add to 11. Its tens digit is three more than its units digit. What is it?

First hint

Call the units digit u.

Second hint

Then u + (u + 3) = 11.

Reveal answer and explanation

The units digit is 4, and the tens digit is 7, so the number is 74.

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NumbersMedium

Ages over time

A parent is three times as old as their child. In 12 years, the parent will be twice as old as the child then. How old are they now?

First hint

Let the child’s age be x.

Second hint

3x + 12 = 2(x + 12).

Reveal answer and explanation

Parent 36, child 12

Solving 3x + 12 = 2x + 24 gives x = 12 and the parent’s age = 36.

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NumbersEasy

The puzzle sale

Four boxes contain six puzzle pieces each. Five pieces are given away. How many remain?

First hint

First find the original total.

Second hint

Calculate 4 × 6 − 5.

Reveal answer and explanation

19 pieces

Four groups of six make 24; removing five leaves 19.

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NumbersEasy

Divisible by three

What is the smallest positive whole number divisible by 3, 4 and 5?

First hint

You need a common multiple.

Second hint

Try the least common multiple of 3, 4 and 5.

Reveal answer and explanation

The prime factors needed are 2 × 2 × 3 × 5 = 60.

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NumbersEasy

Rolling nine

When two ordinary six-sided dice are rolled, how many ordered outcomes give a total of nine?

First hint

List all ordered pairs.

Second hint

The first die can be 3, 4, 5 or 6.

Reveal answer and explanation

Four outcomes

The possibilities are (3,6), (4,5), (5,4) and (6,3).

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NumbersMedium

Sharing a collection

Three friends share 48 puzzles in the ratio 1:2:3. How many puzzles does the friend with the largest share receive?

First hint

The ratio has six parts in total.

Second hint

Find the size of one part.

Reveal answer and explanation

24 puzzles

48 ÷ 6 = 8 puzzles per part. The largest share is 3 × 8 = 24.

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NumbersEasy

The missing total

A four-digit PIN uses the digits 2, 4, 6 and 8 once each. The first digit is 8, the last is 2, and the middle two digits increase from left to right. What is the PIN?

First hint

The two unused digits are 4 and 6.

Second hint

Put them in increasing order.

Reveal answer and explanation

8462

8 _ _ 2 leaves 4 and 6 for the middle positions. Increasing order makes the PIN 8462.

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