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4. Frontline tactics?
Find the smallest natural number with 6 as the last digit, such that if the final 6 is moved to the front of the number it is multiplied by 4.5. Length of a pool
Two kids start a two-length swimming race at the same moment, but from opposite ends of the pool. They swim in lane and at constant speeds, but one kid is faster than the other. They first pass at a point 18.5 m from the deep end and, having completed one length, each child is allowed to rest on the edge of the pool for exactly 45 seconds. After setting off on the return length, the swimmers pass for the second time just 10.5 m from the shallow end.How long is the pool?
6. Killing a Beast
In a land far away, there is a village threatened by an hundred-headed beast. This
beast can only be killed by cutting of all the hundred heads. Legend says that any brave warrior can cut off exactly 10, 20, 30 or 40 heads at one time. However with each of these, 40, 2, 60 and 4 new heads appear respectively.The village has lost several brave warriors against this beast. Can you save the village from this beast ?
7. Coloring a Chess Board
Asterix and Obelix decide to play a game. Th ey pick up a 4x4 board and decide to
color it alternately. Asterix colors white and Obelix black. You can color only fresh
squares, that is, those which have not yet been colored. Whoever is forced to form a 2x2 square of one color is the loser.Asterix, aware of Obelix’ intelligence, allows him to choose who plays first. Your job is to help Obelix choose what to do, so that he does not lose.
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.