Gold Coins

Logic Level 3

You have 10 identical bags containing 10 gold coins each. All of the coins weigh 10 grams, except for the coins in one of the bags which instead weigh 9 grams.

If you have a scale which tells you the total weight of whatever you place on it, then how many weighings are required to determine the bag whose coins are lighter?

Note : You can separate coins from their bag, and you can assume the bags have negligible weight.


The answer is 1.

Md Ansar by Md ansar , 21, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

4 solutions

Md Ansar
Feb 17, 2016

Number each bag from 1 - 10 and take out as many coins as the bag number i.e. from 1st bag 1 coin,from 2nd bag 2 coins . Now weight them it will come out to be less as total coins taken out will be 55 in number and their weight will be 550 gms (if all coins were of 10 gms) . see how much weight is less and it will give you the bag number. Ex- if 8th bag contain 9 gms coins then weighting 55 coins will show 542 gms i.e. 8 grams less this indicates that 8 coins have less weight and bag number is 8 as we have taken out 8 coins from 8th bag.

29 Helpful 0 Interesting 0 Brilliant 0 Confused

Loved the solution!!!!!

Kostis Smanis - 5 years, 3 months ago

Nice explanation!

Akhash Raja Raam - 5 years, 3 months ago

You need to take n coins from nth bag, weight should be 550. You'll get 550 - n total weight, find n, then the nth bag have the 9 grams coins

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kyra Jackson
Feb 21, 2016

Take one coin from each bag and place them on one by one till you get a 9. That coin tells you the bag with lighter coins. Technically you have only weighed once.

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Achille 'Gilles'
Feb 21, 2016

Use the scale only once.

  • Take out 1 coin from bag #1, 2 coins from bag #2, 3 coins from bag #3... 9 coins from #9. There is no need to sample all bags
  • Weight all those coins together.

Having only real coins would give a result of (1+2+3+4+5+6+7+8+9)•10g = 450g but the fakes coins will give you a result off by 1g x number of fake coins... which is the bag number.

According to the result on the scale the fake coin are in this particular bag:

450g - 450g = 0g ➤ bag #10,

450g - 449g = 1g ➤ bag #1,

450g - 448g = 2g ➤ bag #2,

...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...