## Le Monde puzzle [52|solution]

I have now received the first issue of Le Monde magazine, including the solution to puzzle #52 I solved just in time by simulated annealing! The trick is in using the following theorem:

Iter(1,x,y) is divisible by 10x-1 if and only if y is divisible by 10x-1.

Then the value to be found is divisible by 3, but not by 9, by 19, by 29, by 11, by 3 and 7, and by 31. It is thus a multiple of 3x19x29x11x7x31=3,945,711 and only this number satisfies the constraint on Iter(6,1,y).

The first puzzle of the year is as follows:

Select J>999 different numbers ij between 1 and 2001 (1≤jJ) such that (a) if a and b are selected then a+b is selected (assuming a+b<2002) and (b) the residual $\displaystyle{\sum_{\stackrel{1\le k\le 2001}{k\ne i_1,\cdots,i_J}} k}$

is maximised.

### One Response to “Le Monde puzzle [52|solution]”

1. Le Monde puzzle  « Xi'an's Og Says:

[…] the presentation of the first Le Monde puzzle of the year, I tried a simulated annealing solution on an early morning in my hotel room. Here is […]

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