Name
Date
DIRECTIONS: Play higher-or-lower, 1 to 100, with someone. Write down your guesses.
Always guess the middle of what is left.
| Game | The guesses I made, in order | How many |
|---|
Done for you
they picked 61 | 50 (higher) → 75 (lower) → 62 (lower) → 56 (higher) → 59 (higher) → 60 (higher) → 61 (got it!) | 7 |
| 1 | | |
| 2 | | |
| 3 | | |
| 4 | | |
Every guess halves what is left: 100, 50, 25, 13, 7, 4, 2, 1. That is
7 guesses, whatever they picked. One at a time could take 100.
Fill in: how many halvings to get down to one?
| Numbers to search | Guesses, one at a time (worst case) | Guesses, halving |
|---|
| 1. 1 to 10 | 10 | |
| 2. 1 to 100 | 100 | |
| 3. 1 to 1,000 | 1,000 | |
| 4. 1 to 10,000 | 10,000 | |
| 5. 1 to 1,000,000 | 1,000,000 | |
Look down your last column. The first column grows ten times each row. Yours grows by about three.
- A hundred takes 7 guesses and a million takes 20. Say how a task ten thousand times bigger costs only 13 more guesses.
- Halving only works if the numbers are in order. Say what "higher or lower" is doing for you that a shuffled pile could not.
- You have 20 guesses and want the biggest range you could still win on. Work out roughly what it is, and say how you got there.