SOLUTION FOR GOLD COINS:

Step 1: we name all the bag of gold coins as #1, #2, #3......#8, #9, and #10

Step 2: we put 1 coin from bag #1, 2 coins from bag #2, 3 coins from bag #3.........8 coins from bag #8, 9 coins from bag #9, and 10 coins from bag 10 onto the scale. Find out the total weight.

Step 3: the total weight should have been 10 grams X (1+2+3+4+5+6+7+8+9+10=55) = 550 grams if all coins are the same (10grams each).

Step 4: Subtract the total of step 2 from total of step 3.

Conclusion: If step 4 results 1 gram, then bag #1 is the low quality coins, if step 4 results 2 grams, then bag #2 is the one, if step 4 results 3 grams, then bag #3 is the one.......etc.

Thanks to Jason Vuong for this variation!

 

 

***Special Note:  Another visitor, Jay, offers this solution to this problem.  Perhaps an easier way to look at it?!  Read on and see what you think:

1. I would put one coin on the scale from one of the bags.

2. If the change in weight on the scale is 10 grams, I 'd add a coin from another bag.

3. I'll keep on adding a coin from each bag until the change in the total weight after adding a coin is by 9 grams and the bag that coin comes from is the low quality one.

I just made it look big and in 3 different steps to make it sound easier but in practicality it's really simple and I believe even a 3 year old kid can do it.

Thanks Jay!!

AND, ANOTHER VISITOR, Luis, POSES THIS:

I write you regarding weighty problem No.2 (gold coins) I believe that Jay's solution to this problem does not follow the restriction on the use of the scale. The first coin you place on the scale will give a reading, this will count for one use of it, so you would not be able to place another coin on it because this will give you a second reading, resulting in a second use of the scale.

 

    

 

 

 

 

 

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