Games and Winning Strategies
Class 6 Maths · Chapter 3: Number Play · NCERT Ganita Prakash section 3.12
Learn
Race to 20: the first player says 1 or 2. Then players take turns adding 1 or 2 to the total. Whoever says 20 wins.
Play against your study buddy! Can you find the secret?
The secret: work backwards from 20. If you say 17, your friend can only reach 18 or 19, and then you reach 20. So 17 is a winning number, and so are 14, 11, 8, 5 and 2: each is 3 less.
Game 2: add 1 to 5 each turn; first to 50 wins. Now the winning numbers jump by 6: 2, 8, 14, 20, 26, 32, 38, 44, 50.
Remember
- Work backwards from the winning number.
- If you can add 1 to k, the winning numbers are k + 1 apart.
Quick check
In the race to 20 (adding 1 or 2), which number should you say so that you are sure to win?
- 15
- 16
- 17
- 18
Answer
17. After 17 your friend can reach only 18 or 19, and then you say 20.
Think about it
Race to 30: players add 1, 2, 3 or 4 each turn. Should you go first or second? What is your plan?
One answer
The winning numbers are 30, 25, 20, 15, 10 and 5 (each 5 less). The first player cannot say 5 straight away, so go second: whatever your friend adds, add enough to make 5, then 10, 15, 20, 25 and 30.
Practice
Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.