Problem: Prove that p2 – 1 is divisible by 24 if p is a prime number greater than 3? Solution: The most elementary proof , without explicitly mentioning any number theory: out of the three consecutive numbers p–1, p, p+1, one of them must be divisible by 3; also, since the neighbors of p are … Read More →
Possible Paths across a Rectangular Grid
Problem: Consider a rectangular grid of 4×3 with lower left corner named as A and upper right corner named B. Suppose that starting point is A and you can move one step up(U) or one step right(R) only. This is continued until B is reached. How many different paths from A to B possible ? Now let’s … Read More →
Age of 3 children – Mathematical Puzzle
Problem: Two old friends, Jack and Bill, meet after a long time. Jack: Hey, how are you man? Bill: Not bad, got married and I have three kids now. Jack: That’s awesome. How old are they? Bill: The product of their ages is 72 and the sum of their ages is the same as your … Read More →
100 Doors Puzzle
Puzzle: : You have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the … Read More →
IIT Students and Hats Puzzle
Puzzle: The riddle is Nine IIT students were sitting in a classroom. Their professor wanted them to test. Next day the professor told all of his 9 students that he has 9 hats, The hats either red or black color. He also added that he has at least one hat with red color and the … Read More →
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