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Showing posts from April, 2010

### Oleg Kryzhanovsky’s Problem - Coin Sequence

Source: http://blog.tanyakhovanova.com/ Problem: You have 6 coins weighing 1, 2, 3, 4, 5 and 6 grams that look the same, except for their labels. The number (1, 2, 3, 4, 5, 6) on the top of each coin should correspond to its weight. How can you determine whether all the numbers are correct, using the balance scale only twice? Disclaimer: It is a difficult problem Hint: (Highlight from * to * to see the hint) * Some people post wrong solutions and believe they have solved it. For example, they would start by putting the coins labeled 1 and 2 on the left cup of the scale and 3 on the right cup. If these coins balanced, the person assumes that the coins on the left weighed 1 and 2 grams and that the coin on the right weighed 3 grams. But they’d get the same result if they had 1 and 4 on the left, for example, and 5 on the right. I propose the following sequence a(n) . Suppose we have a set of n coins of different weights weighing exactly an integer number of grams

### Weighing Piles of Coins

Source: Asked to me by Ankush Agarwal (Sophomore, CSE, IITB) Problem: There are two kinds of coins, genuine and counterfeit.  A genuine coin weighs X grams and a counterfeit coin weighs X+delta grams, where X is a positive integer and delta is a non-zero real number strictly between -5 and +5.  You are presented with 13 piles of 4 coins each.  All of the coins are genuine, except for one pile, in which all 4 coins are counterfeit.  You are given a precise scale (say, a digital scale capable of displaying any real number).  You are to determine three things: X, delta, and which pile contains the counterfeit coins.  But you're only allowed to use the scale twice! Prize: Treat at H8 canteen to the first person who solves it!!