Calculator Tricks 5

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Calculator Tricks 5

• By
• Brian Carruthers

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The 421 Loop

• Pick a whole number and enter it into your
  calculator.
• If it is even, divide by 2.
• If it is odd, multiply by 3 and add 1.
• Repeat the process with the new number over and
  over.

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What happens?
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The sequence always ends in the loop

• 421421

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For Example Lets Start with 13

• 13 is odd, so we multiply by 3 and add 1.
• We get 40. (13 x 3 39 1 40)
• 40 is even, so we divide by 2 . We get 20. (40 /
  2 20)

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• 20 is even, so we divide by 2 and get 10.
• 10 is also even, so we divide by 2 again and get
  5.

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5 is odd so we multiply by 3 and add 1.

• We get 16.
• 16 is even, so we divide by 2 and get 8.
• 8 is also even, so we divide by 2 again and get
  4.

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• 4 is even, so we divide by 2. We get 2.
• 2 is even, so we divide by 1 and get 1.
• 1 is odd, so we multiply by 3 and add 1.
• We get 4.
• 4 is even , so we divide by 2.
• We get 2.
• 2 is even, so we divide by 1.
• We get 1.

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And so we begin the loop

• 421421

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Now what did you think

• of that?