Suppose you have an infinite stock of $a bills and $b bills such that g.c.d(a,b)=1. Find the largest amount of money (integer) that cannot be represented using $a and $b denominations.

- via Wolfram Mathematica

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Suppose you have an infinite stock of $a bills and $b bills such that g.c.d(a,b)=1. Find the largest amount of money (integer) that cannot be represented using $a and $b denominations.

- via Wolfram Mathematica

There are 3n checkers: n red, n green, n blue. They are shuffled and placed on an n x 3 board. Your objective is to rearrange the checkers so that each of the n columns has one each of red, green and blue checkers. However, you are allowed to swap checkers only if they are in the same row. Is it possible to achieve your objective?

- via Algorithmic puzzles

A knight is in one corner of a 100x100 chessboard. What is the minimum number of moves needed to go to the diagonally opposite corner?

- via Algorithmic puzzles

A gift card of $5 is auctioned between two people. The rules are strange. The players are allowed to bid forever until both of them are unwilling to bid higher. However, each player has to pay the highest bid that (s)he made whether or not he wins the $5 gift card. Of course the gift card goes to the higher bidder. Will the bidding ever stop?

You are given a string of the form "?<?>?>?<...<?", containing n '?' symbols. Give an algorithm to replace each '?' by a unique integer from 1 to n such that all the inequalities in the string are satisfied. For example, if the given string is "?<?>?>?", your algorithm may return "2<4>3>1", but may not return "4<3>2>1".

- via Algorithmic puzzles

Suppose a sequence of natural numbers satisfies the following:

1. The sequence is strictly increasing.

2.

3. If m,n are relatively prime, .

Show that the only such sequence is .

- via Mind your decisions

Find the area of a single triangle in the figure below (all triangles are right-angled).

Hint: If you use geometry rather than algebra, you will find this a challenging puzzle. That's why there are 4 triangles. Try to rearrange them.

- via Mind your decisions

An ant enters a spherical fruit at one point on the surface and exits at another point on the surface. In this process, the ant digs a trail of length 61 cm (not necessarily a straight line). The diameter of the fruit is 62 cm. Show that the trail must lie completely in one hemisphere.

- via WU Riddles

An Arab sheikh tells his two sons to race their camels to a distant city to see who will inherit his fortune. The one whose camel is slower will win. The brothers, after wandering aimlessly for days,ask a wise man for advise. After hearing the advice they jump on the camels and race as fast as they can to the city. What does the wise man say?

- via Brain Den