Expert: Rohit Agarwal - 10/2/2007

Question
QUESTION: Hi, my name is Jennifer and i need help for this brainteaser.
I've working on it for days but still cant get it.

Question: You are trapped in a room with no windows or doors.  In the room are 10 very large barrels heaped unevenly with gold coins.  Every barrel contains coins with a mass of gm except one whose coins have a mass of 0.9g.  
You are given a digital scale, but it will only give you one correct reading.  After that one reading, the number on the screen will not change, no matter what you do to it. This means you only have one chance to measure the coins.
How can you use the scale to determine which barrel contains the lighter coins?
You can not feel the difference yourself, only the scale will notice the difference, no matter how many coins you pick up.


ANSWER: Hi... This is a relatively easy problem (compared to the others I've encountered).

You put the following coins on the balance:

1 coin from the 1st heap
2 coins from the 2nd heap
2 coins from the 3rd heap
...
10 coins from the 10th heap

Now you look at the fractional part of the reading of the digital scale.

If it is 0, our answer is heap 10
If it is 1, our answer is heap 9
It it is 2, our answer is heap 8
...
If it is 9, our answer is heap 1

hope it helps...

---------- FOLLOW-UP ----------

QUESTION: Yes, thank you, but the scale can only be used ONCE.That is the problem, please help!

Answer
I'm sorry if I didn't make the solution clear before. What I meant to say was that keep the following items together on the scale (all at once).

1 coin from the 1st heap
2 coins from the 2nd heap
3 coins from the 3rd heap
...
10 coins from the 10th heap

So, you should be weighing 1+2+3+...+10(=55) coins at a time at once. And this is the ONLY weighing that you will require to determine which heap has the lighter coins.

If the scale reads 54.9, our answer is heap 1
If the scale reads 54.8, our answer is heap 2
If the scale reads 54.7, our answer is heap 3
...
If the scale reads 54.0, our answer is heap 10

hope this helps...