By David, 28 December 2015 Activity

- The board game ‘Guess Who’ or a similar game. If you don’t have a copy, you could use a large box to hide your numbers from your opponent.
- Three printed copies of the ‘Guess my number’ sheet: you can download it here
- Scissors
- Someone to play with

- Take all of the game’s people out of the two flip boards.
- Cut out the 24 rectangles from one of the sheets you printed out. Insert one rectangle into each slot in one flipboard.
- Cut out the rectangles from a second sheet and insert them into the second flipboard.
- Cut out the rectangles from the third sheet to make a pile of number cards.

- Give each player a flipboard, and flip all the numbers up.
- Shuffle the pile of number cards. Each player draws one number card. Keep your number card hidden from your opponent!
- The aim of the game is to guess your opponent’s number card before they guess yours.
- Take it in turn to ask each other ‘yes’ or ‘no’ questions. For example, you could ask: ‘Is your number even?’
- When your opponent replies, you can eliminate numbers that don’t match. For example, if they reply ‘No’ to the question in Step 4, you can flip down all the even numbers on your flipboard.
- When you think you know which number your opponent has, ask them if they have that number. If you’re right, you win!

- Is your number odd?
- Does your number have two digits?
- Is your number bigger than 15?
- Does your number have the digit 1 in it?
- Is your number a prime number?

You can use two different strategies when you’re playing this game.

One way is to ask questions that split the field in half. For example, you could ask: “Is your number even?” or “Is your number bigger than 12?”

The other way is to ask very specific questions that have a small chance of eliminating lots of numbers. These sorts of questions could include: “Is your number bigger than 20?” or “Is your number a square number?”

Which of these strategies is the best? If you always divide the group in half, or close to, you can find the opponent’s number in four or five turns. If you use specific questions, you could either find out the answer faster, or much slower. The most specific strategy you can use is to simply ask: “Is your number 1?”, “Is your number 2?”, and so on. Using this strategy, you could take up to 23 turns to work out your opponent’s number, and on average, you would take about 12 turns.

Finding the best strategy in Guess Who (video)

For more advanced mathematicians, try the ‘Guess my hard number’ sheet, which you can download here

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