Challenge 13: Numerical Recycling
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Video Responses
Spoiler Alert! Video responses include explanations of how to solve the challenge problem. We recommend that you resist the temptation to watch response videos until after you have explored the challenge individually or with a problem solving team!
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Jacob's observations on the problem, using a computer program to automate data collection!
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Follow-up video from Jacob, with further results and observations.
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Three trials from Ms. Pupillo's 4th graders at Saul Mirowitz Jewish Community School.
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Follow-up Challenges
- Suppose we change Step 1 of the procedure so that we cube the number (instead of squaring). How would this change the overall behavior of the machine?
- Suppose we change Step 2 of the procedure as follows: If the digit-sum has more than one digit, find its digit sum. Continue until the result has just one digit and pass this single digit back to Step 1. For instance, if we get the number 256 in Step 2, we find the digit sum 2+5+6 = 13. The sum has more than one digit and so we do the digit-sum step again: 1 + 3 = 4. We send the result 4 back to Step 1. How would this change the overall behavior of the machine?
