Wednesday, August 24, 2005

The JFE 8555 problem

The Sum of Digits:


On the 28th of July, blogger JFE 8555 highlighted an interesting phenomenon to do with the digits of numbers.

See this for the original version by the author himself itself.

Below is an example done using a 5-digit number, 35997.

We will attempt to add the digits together in any arbitrary manner, repeating till we reach one digit.

35897
-> 3 + 5 + 8 + 9 + 7 = 32
-> 3 + 2 = 5

(35) + (897) = 932
-> 9 + 3 + 2 = 14
-> 1 + 4 = 5

(3+5) + (8 + 9) + 7 = (8) + (17) + 7
-> 8 + (1+7) + 7 = 8 + 8 + 7
-> 8 + 8 + 7 = 23
-> 2 + 3 = 5

3 + 58 + 97 = 158
-> 15 + 8 = 23
-> 2 + 3 = 5


The flabbergasted reader might want to try a few other combinations for amazement’s sake.

Tomorrow, the explanation!




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