Discrete Maths puzzles




Medium Discrete Maths

An 8x8 chessboard can be entirely covered by 32 dominoes of size 2x1. Suppose we cut off two opposite corners of chess (i.e. two white blocks or two black blocks). Prove that now it is impossible to cover the remaining chessboard with 31 dominoes.

Hint
Solution
Source: Martin Gardner
Enable Like and Comment


Medium Discrete Maths

13 Apples, 15 Bananas and 17 Cherries are put in the magic hat. When ever a collision of two different fruits occurs, they both get converted into the third type. For example 1 Apple and 1 Banana can collide to form 2 cherries. No other collision is holy. Can a sequence of such magical collisions lead all 45 fruits to give just one type?

Hint
Solution


Medium Discrete Maths

There are 51 ants sitting on top of a square table with side length of 1. If you have a square card with side 1/5, can you put your card at a position on the table to guarantee that the card encompasses at least 3 ants?

(updated: square card was originally disk of radius 1/7)

Hint
Solution


Medium Discrete Maths

On a 2D complex plane, all the integer-component points are coloured either White or Black. Is Possible to find a rectangle parallel to axis which has all corners of same color?

Solution
Source: Top Quant Interview
Enable Like and Comment


Medium Discrete Maths

In a circle are light bulbs numbered 1 through n, all initially on. At time t, you examine bulb number t, and if it’s on, you change the state of bulb t + 1 (modulo n); i.e., you turn it off if it’s on, and on if it’s off. If bulb t is off, you do nothing. Prove that if you continue around and around the ring in this manner, eventually all the bulbs will again be on.

Hint
Solution
Source: P. Winkler
Enable Like and Comment




© BRAINSTELLAR