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Problems in Issue 11.2
0. You are given 25 horses and you have to find the three fastest amongst them, using a series of races. In each race, you can race five horses against each other and the only information you get is their relative positions at the end of the race. What is the minimum number of trials required for you to find the three fastest horses?
1. In this chess problem it is White's turn to move. Give a sequence leading to checkmate in four moves [that is, White-Black-White-Black-White-Black-White (checkmate)].
2. Give a partitioning of positive integers into infinite subsets, each having infinite elements, such that every subset A can be obtained from any other subset B by adding a constant to every? element of B.
Hints
0. The answer is less than 10:)
1. You'll have to move only two different pieces as White
2. Any integer ABCD can be written as A0C0 + B0D. Extend this property to all integers, and construct two sets
PREVIOUS PROBLEMS
In this section, you can browse through the problems that have appeared in previous issues of InsIghT, get hints and see the solutions.