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Calculator Tricks 6

Calculator Tricks 6. By Brian Carruthers. The 6174 Loop. Select a four-digit number using four different digits. (Don’t use 1111 or 2222 etc.) Arrange the digits in increasing order. Now arrange the digits in decreasing order. Subtract the smaller numbers from the larger number.

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Calculator Tricks 6

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  1. Calculator Tricks 6 By Brian Carruthers

  2. The 6174 Loop • Select a four-digit number using four different digits. • (Don’t use 1111 or 2222 etc.) • Arrange the digits in increasing order. • Now arrange the digits in decreasing order. • Subtract the smaller numbers from the larger number.

  3. Repeat steps 2, 3, and 4 • with the result, and so on. • What happens?

  4. Let’s try, say, 7173 • Arrange the digits in increasing order: 1377 • Arrange the digits in decreasing order: 7731 • Subtract the smaller number from the larger number.

  5. 7731-1377 = 6354 • Repeat the process with 6354 • 6543 – 3456 = 3087 • 8730 – 0378 = 8352 • 8532 – 2358 = 6174 • 7641 – 1467 = 6174 • 7641 – 1467 = 6174 • 7641 – 1467 = 6174 (we’re in a loop)

  6. Amazingly, all four-digit numbers except: • multiples of 1111 • end up in the 6174–loop. • No real reason has yet been found for this phenomenon.

  7. Now! What did you think of that?

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