**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).

**T**he first puzzle of the year is as follows:

*Select *J*>999 different numbers i*_{j} between 1 and 2001 (1≤j*≤*J*) **such that (a) if a and b are selected then a+b is selected (assuming a+b<2002) and (b) the residual*

*is maximised.*

Filed under: R, Statistics Tagged: Le Monde, mathematical puzzle, simulated annealing

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**Tags:** Le Monde, mathematical puzzle, R, simulated annealing, statistics