 |
| http://www.suzannesutton.com/_borders/man_thinking_numbers.jpg |
A mind-reading trick
Many amusing "mind-reading" tricks have simple mathematical explanations. Suppose you ask a friend to think of a number and keep it a secret. Then ask him - to multiply his number by 5, add 6, multiply 4, add 9, and multiply by 5. Now ask him to tell you the result. When he does, you need only moment's thought to tell him his original number.
Suppose you friend chooses 13. He multiplies by 5: 13 x 5 = 65. He adds 6: 65 + 6 = 71. He multiplies by 4: 71 x 4 = 284. He adds 9: 284 + 9 = 293. And he multiplies by 5: 293 x 5 = 1465. He tells you the number 1465. Without telling him, subtract 165 from the number he tells you , divide by 100 (drop two zeros) and tell him his original number. In the case of 1465, subtract 165: 1465 - 165 = 1300. Divide by 100: 1300 / 100 = 13. You can explain the trick by using n to represent the unknown number: Here are the steps.
1. n
2. 5n
3. 5n + 6
4. 4(5n + 6) = 20n + 24
5. 20n + 24 + 9 = 20n + 33
6. 5(20n + 33) = 100n + 165
So 100n + 165 equals x, or the number your friend tells you. You solve 100n + 165 = x by subtracting 165 from x and dividing it by 100. No matter what number your friend chooses, you can find it by following the rule given above.
1 comments:
Post a Comment