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Another riddle

one

RefChat Addict
Level 7 Referee
Riddles the order of the day, have a shot at this one from my early years. It is not a trick or silly question.

9 bags each has 100 fake gold coins. And one other bag with 100 real gold coins. All coins and bags are identical in every way except for coin weight. All fake gold coins are 100 grams. All real gold coins are 110 grams.

We have an accurate scale but we have to find the real gold coins by only one weighing (one weight reading). How is it possible?
 

Mr Dean

Active Member
- Name the ten bags 0-9.
- Take 0 coins from Bag 0, 1 coin from Bag 1, 2 coins from Bag 2,..., and 9 coins from Bag 9.
- Weigh all the coins you have taken.
- The weight of the coins is a four digit number; the second to last digit of that number represents the bag which contains the real coins.
 
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Sheffields Finest

Maybe I'm foolish, maybe I'm blind!
Level 7 Referee
Label the bags from 1 to 10. Take 1 bead out of Bag 1, and label it 1. Take 2 beads out of Bag 2, and label them both with a 2. Take 3 beads out of Bag 3, and label each with a 3. Continue this pattern with Bags 4 to 10. Put these 10 beads on the tray of the scale.

If all 20 weighed 10 grams, the scale would register 200 grams. But since one or more of the beads weighs only 9 grams, the scale will register less than 2000. Subtract the number on the scale from 200. Your answer will tell you the number of the bag with the lighter beads. (If the scale registers 200, it's bag #2)
 

one

RefChat Addict
Level 7 Referee
Label the bags from 1 to 10. Take 1 bead out of Bag 1, and label it 1. Take 2 beads out of Bag 2, and label them both with a 2. Take 3 beads out of Bag 3, and label each with a 3. Continue this pattern with Bags 4 to 10. Put these 10 beads on the tray of the scale.

If all 20 weighed 10 grams, the scale would register 200 grams. But since one or more of the beads weighs only 9 grams, the scale will register less than 2000. Subtract the number on the scale from 200. Your answer will tell you the number of the bag with the lighter beads. (If the scale registers 200, it's bag #2)
Answer to the wrong question. Needs a bit of work either way ;)
 

Russell Jones

RefChat Addict
Level 3 Referee
Label the bags from 1 to 10. Take 1 bead out of Bag 1, and label it 1. Take 2 beads out of Bag 2, and label them both with a 2. Take 3 beads out of Bag 3, and label each with a 3. Continue this pattern with Bags 4 to 10. Put these 10 beads on the tray of the scale.

If all 20 weighed 10 grams, the scale would register 200 grams. But since one or more of the beads weighs only 9 grams, the scale will register less than 2000. Subtract the number on the scale from 200. Your answer will tell you the number of the bag with the lighter beads. (If the scale registers 200, it's bag #2)
I've heard of turning wine into water but not sure turning gold coins into beads is going to catch on in the same way .... :rolleyes:
 
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