Princess in a Palace
A princess is living in a palace which has 17 bedrooms, arranged in a line. There is a door between
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A princess is living in a palace which has 17 bedrooms, arranged in a line. There is a door between
The white king has made himself invisible. Where is he?
Design a game that takes less than 35 moves to get to the position below.
A prince decides to get married to the prettiest girl in his kingdom. All 100 available ladies go to the palace and show themselves to the prince one by one. He can either decide to marry the girl in front of him or ask her to leave forever and call the next one in line. Can you find a strategy which will give the prince a chance of 25% to get married to the prettiest girl? Can you find the best strategy?
Remark: Assume that the prince can objectively compare every two girls he has seen.
Two monks are standing on the two sides of a 2-dimensional mountain, at altitude 0. The mountain can have any number of ups and downs, but never drops under altitude 0. Prove that the monks can climb or descend the mountain at the same time on both sides, always staying at the same altitude, until they meet at the same point.
There are a fly and three spiders on the edges of a cube. If the spiders’ velocities are at least 1/3 of the fly’s velocity, and all insects can travel only along the edges of the cube, show that the spiders can eventually catch the fly.
What is the largest number of pieces you can slice a doughnut into using only 3 cuts? You are not allowed to rearrange the pieces between the cuts.
A large rectangle is partitioned into smaller rectangles, each of which has integer length or integer width. Prove that the large rectangle also has integer length or integer width.
It is well known how to split fairly a cake between two people – one of them cuts, the other one picks. The question is, how can you split fairly a cake between three people?
Easy: “Fairly” means that every person gets at least 1/3 of the cake.
Hard: “Fairly” means that every person has the opportunity to get at least as much
Is it possible to design a simple closed curve inside a box, such that its projections on all 6 walls of the box are trees, i.e. curves without loops?
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