Avanade Interview Question: You have 100grams of gold to ... | Glassdoor

# You have 100grams of gold to distribute evenly among

10 goldsmiths. They are each to make 10 coins of 1 gram each. When you get them back, you know one goldsmith is making coins of 0.9 grams and keeping the rest. Measuring the least amount of times how would you determine which smith is cheating?
Tags:
analytical

2

The most common answer, and the one I gave, is eliminate half of the smith, then half of the remaining and so on. However, there is a way to determine the culprit by measuring only once.

Interview Candidate on Jun 4, 2010
27

You need only one measurement; together, measure 1 coin from smith A, 2 coins from smith B, 3 coins from smith C,..., and 10 coins from smith J. You know which smith ripped you off by the amount missing; total weight with accurate coins would be 55 grams. For example, if the scale read 54.7 grams you would know that smith C was the culprit since exactly .3 grams were missing (3 coins).

Anonymous on Oct 5, 2010
0

You can do this with maximum 3 measurements. Weight 5 coins on each balance and see which one is lighter. So now you know out of which 5 coins you have the culprit. Now again weigh 2 coins on each balance, keeping one left coin with you. If they weight equal, you know the lightest coin is the one in your hand. If not, then you know out of which 2 coins is the lightest one. You can weigh them and see which is the one.

Amruta Madankar on Sep 19, 2015
0

You can do this with maximum 3 measurements. Weight 5 coins on each balance and see which one is lighter. So now you know out of which 5 coins you have the culprit. Now again weigh 2 coins on each balance, keeping one left coin with you. If they weight equal, you know the lightest coin is the one in your hand. If not, then you know out of which 2 coins is the lightest one. You can weigh them and see which is the one.

Amruta Madankar on Sep 19, 2015