Recreational Math

Just For Fun

What is number guessing?

Number guessing is a game (some say trick). Some people can do number guessing in their heads, as long as the numbers are kept small. Have a person think of any positive integer n (not zero or any negative numbers) and apply the following steps:

  1. For example, a person chooses the number 25 and keeps that number to him- or herself. Ask the person to compute 3 × n. (3 × 25 = 75)
  2. Ask if the number is odd or even. (odd)
  3. If the number is even, tell him or her to divide the number by 2; if the number is odd, tell him or her to add 1 to the number, then divide that number by 2. (75 + 1 = 76/2 = 38)
  4. Tell him or her to take that number and multiply by 3, then divide by 9. (38 × 3 = 114/9 = 12.666 …)
  5. Take that number and multiply by 2 (12.666 … × 2 = approximately 25). The answer should be the original number—or close to it.


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