Discrete Maths puzzles




Hard Discrete Maths

We have a beam balance (with two pans to compare weights) and a positive integer N. How do we select fewest number of pebbles to weigh all possible integers from 1 to N

Solution


Hard Discrete Maths

Several gas stations on a circular trek have between them just enough gas for one car to make a complete round trip. Prove that if you start at the right station with an empty tank you shall be able to make it all the way around.

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Solution
Source: P. Winkler
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Hard Discrete Maths

Can you pack 53 bricks of dimensions 1x1x4 into a 6x6x6 box? The faces of the bricks are parallel to the faces of the box

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Answer
Solution
Source: Xinfeng Zhou
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Medium Discrete Maths

There is a crazy clock in Alice's Dream, it has two hands initially pointing at 12. The minute hand moves clockwise, making 5 rounds (with varying speeds) and comes back to 12. In the same time, the hour hand goes anti-clock wise, finishing 4 rounds and returns to 12. How many times did the two cross each other ? (Cross means meet & pass through, hence ignore start & end)

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Solution


Medium Discrete Maths

A group of students are sitting in a circle with the teacher in the center. They all have an even number of candies (not necessarily equal). When the teacher blows a whistle, each student passes half his candies to the student on his left. Then the students who have an odd number of candies obtain an extra candy from the teacher. Show that after a finite number of whistles, all students have the same number of candies.

Hint
Solution
Source: puzzletweeter
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