$n(n+1)/2$ coins are placed on an equilateral lattice with side $n$, such that all but one coin are showing heads.
At each step, one is allowed to choose two adjacent coins $A$ and $B$, and then flip all coins on the line $AB$ (and its extension).
Characterize all starting configuration such that it's always possible to get all tails.
Showing posts with label coin. Show all posts
Showing posts with label coin. Show all posts
Tuesday, March 1, 2011
Thursday, March 18, 2010
Which stack has counterfeit coins?
Credit to this problem goes to MIT Technology Review Puzzle Corner, November/December 2009 Edition.
Given thirteen stacks each containing four coins, we are told that exactly one stack contains all counterfeit coins. A counterfeit coin weighs less than a good coin by an amount not exceeding 5 grams, and all good coins weigh an integral number of grams.
We are given a precision scale with a very wide area to put the coins on. We need to answer all these three questions all in two weighings:
1. What is the weight of a good coin?
2. What is the weight of a counterfeit coin?
3. Which stack has the counterfeit coins?
Given thirteen stacks each containing four coins, we are told that exactly one stack contains all counterfeit coins. A counterfeit coin weighs less than a good coin by an amount not exceeding 5 grams, and all good coins weigh an integral number of grams.
We are given a precision scale with a very wide area to put the coins on. We need to answer all these three questions all in two weighings:
1. What is the weight of a good coin?
2. What is the weight of a counterfeit coin?
3. Which stack has the counterfeit coins?
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