[Community Puzzle] Her Majesty's well shared secret

Hello,

I would like to know if i really understood the algo.

First of all, all the difficulty is to find the “random number” generate.
The thing with the multiple compute is because you have k-1 possibilities, so you have to choose a number that led you have the good tuple for every agents ?

The thing is we have 3 numbers to find, but only 2 equations :
[ (X1 * X + number1) %53, (X2 * X + number2) %53, (X3 * X + number3)%53 ] = [Y1,Y2,Y3]
[ (X1 * 2 * X + number1)%53, (X2 * 2 * X + number2)%53, (X3 * 2 *X + number3)%53 = [Y4,Y5,Y6]

With only Y1,Y2…,Y6, how can we know X1,X2…,X6 and the 3 numbers number1, number2 and number3 ?

Thx

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