Solution for The Gold Coins Puzzle
Here's the solution to the gold coins puzzle. Some of our visitors came up with some nice variations for the solution and we have posted them.
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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