Materials:
Pail of water, ashtray, matches, bar of soap
Before students arrive:
Choose a number between 10 and 49, for example 15.
Using the bar of soap, write the number you have
chosen on the back of your hand.
Now subtract that number from 99.
(For example, 99 - 15 = 84).
When students arrive:
1. Have students choose a number between 50 and 99.
2. Have them add 84 (your answer from above) to that number.
3. Cross out the hundreds digit and add one to the units digit.
4. Subtract the answer from the original number.
5. Have one student write his answer on a folded piece
of paper, fold into fourths, and hand it to you.
6. Burn the folded answer in the ashtray.
7. Rub the ashes on your hand, then dip your hand in water.
8. To the students' amazement, the answer "appears" on your hand!
Example:
| 1. Have students choose a number between 50 and 99. | Let's say the students chose 72. |
| 2. Add 84 (your answer from above) to that number. | Then they get 72 + 84 = 156 |
| 3. Cross out the hundreds digit and add one to the units digit. | Cross out the 1 and add it to 56 to get 57. |
| 4. Subtract the answer from the original number. | They should get 72 - 57 = 15. |
Why does this work?
Here is a proof for the example above:
| 1. Have students choose a number between 50 and 99. | Let x = tens digit and y = ones digit So the number would be 10x + y |
| 2. Add 84 (your answer from above) to that number. | Then they get 10x + y + 84 |
| 3. Cross out the hundreds digit and add one to the units digit. | Crossing out the hundreds digit is the same as subtracting 100, so the number would be 10x + y - 16 Adding 1 to the number becomes: 10x + y - 15 |
| 4. Subtract the answer from the original number. | They should get (10x + y) - (10x + y - 15) = 10x + y - 10x - y + 15 = 15 |