perplexus.info :: Numbers : Less than 100

Less than 100 (Posted on 2021-02-14)

Pick up at random a 3-digit number and decrease it by the sum of its digits.
Clearly,applying this procedure again and again you will hit zero no matter how big your initial number was .
How many iterations at most are needed and how many numbers cause it?

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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related OEIS entry

Comment 3 of 3 |

http://oeis.org/A309417

Term 3 = 81 implies 10^3=1000 takes 81 iterations.

Since The first iteration takes 1000 to 999,

999 takes 80.

Every number from 999 to 990 reduces to 972, these all require 80.

(The decade 989 to 980 reduce to 963 and so get there faster.)

Posted by Jer on 2021-02-14 09:43:40

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