Here’s a question I got from my father:

In front of you are 6 bags, each one of them has 10 gold coins. 1 of these bags, however, is filled with coins with a slight impurity. The gold coins all weigh 1 ounce, while the impure coins weigh 1.01 ounces. You have a scale (a scale, not a balance, so this thing just tells you how much something weighs). You are allowed to make only 1 weight measurement. How can you determine which bag has the impure coins?

Difficulty Rating: 14

This might be me making up rules (that you can take coins out of the bags) again, but I’m going to answer before asking so as to be first if I’m right:

Assign the bags numbers from 1 to 6, then take that number of coins out of each bag and put them on the scale (presumably you could lay them out on the scale so that you can keep track of which are which and return them to their original bags if need be). The total weight will be 21 ounces plus .0n, where n is the number you assigned to the bag that contains the impure coins.

maybe…

put all 6 bags on the scale. take one off at a time and watch the weight go down each time until you have a winner? (does that count as one measurement?)

Just to clarify: “1 weight measurement” can be thought of as “1 number”.. As though you were telling someone else to do the actual measuring, and all you are given is what that weight was. 1 weight, 1 number, 1 try.

Weigh together 1 coin from the first bag, two coins from the second, three from the third, four from the fourth, 5 from the fifth and 6 from the 6th. The result will be 21.0? where the ? will be one of the numbers 1-6. Whatever the ? is, is the bag with the impure coins.

I need the points, I think.

1 from bag 1

2 from bag 2

3 from bag 3

4 from bag 4

5 from bag 5

6 from bag 6.

The decimal point tells you which bag. i.e x.01=bag 1; x.02=bag 2; etc.

label bags 1 through 6 take 1 coin from bag 1 two coins from bag 2 and so on until 6 coins from bag six. weigh coins together and whatever the total is the last number will tell you which bag is the impure bag. ex. if the total is 202 it would be bag 2 or 204 it would be bag 4 and so on.