Post Archives from the ‘Puzzles’ Category
7 is a prime number and 7+1=8 is a perfect cube. Can you find another prime number p such that p+1 is a perfect cube? - via Daily Brain Teaser
Suppose you have an array of size n, where each element in the array is either 0, 1 or 2. How will you compute the minimum number of swaps required to sort the array in O(n) time? - via Algorithmic Fest at Stanford
You are given an array of n distinct integers. A swap is interchanging the value of two positions in the array. What is the minimum number of swaps required to sort the array? For example: If the array is [2,1,3], we need only 1 swap (swap 1 and 2). If the array is [2,3,1], we need 2 swaps (swap 2 and 3, then swap 1 … Continue reading the story "Sorting"
Can you move two sticks so that the fly is outside the glass? -via Best Brain Teasers
There are n people standing in a circle. Staring with person 2, every second person is eliminated until only 1 person survives. Who is the survivor? Example: If n=7, people are killed in the order 2,4,6,1,5,3 and person 7 survives. If n=5, persons are killed in the order 2,4,1,5 and person 3 survives. - via Wikipedia
Show that every convex polygon of area 1 is contained in some rectangle of area 2. - via AMS puzzle corner
A 9x9 grid is filled with numbers from 1 to 81, each number occurring exactly once. The grid is said to be ultramagic if the product of numbers in row k is equal to the product of numbers in column k for each k. Can you construct an ultramagic grid? - via AMS puzzle corner
Joe owes $100 to creditor A, $200 to creditor B and $300 to creditor C. Joe dies, leaving behind an estate. Unfortunately, Joe's estate has insufficient funds to repay his creditors (yes, that's a very small estate). The question is how does one split the estate among the contestants. Here are three situations and the action by a certain judge in each situation: 1. If the … Continue reading the story "Talmud problem"
You have a jar with 20 black balls and 16 white balls. At each step, 1. You remove two balls. 2. If the two balls are of the same color, you add a black ball. Otherwise you add a white ball. You repeat these steps until there is only 1 ball remaining in the jar. What is the color of the remaining ball? As a follow-up question, suppose you … Continue reading the story "Removing balls"