## Monday, December 19, 2011

### Mindbender

My friend across the pond posed the following:

So, being a baby wonk, I constructed a table:

This consists of numbers 1-98, the sum of the digits, that sum * 17 +1. The difference between the result at the first number. This gives the following plot:

As you can see, rather than ever having a zero value, it is monotonically increasing (in a sort of interesting way).

So, I doubt if one can find such a number.
Unless, on simple adds the number of digits as in this table:

Clearly the only number that would fit is 35 since by the time one gets to six digits the sum*17 + 1 is only 103.

I haven't looked at the answer. I'm probably wrong. In which case, I will slink away.

Ah, Ha! The Wizard across the pond shows me up. Of course I didn't extend my calculations beyond 100. If I had, I would have gotten the following graph of the difference:

What appeared from 1 to 99 as a dull, monotonically increasing pattern was part of a bigger pattern going the other way. (I should take it beyond 1000.)

When the difference is taken gives this graph: