Post: 1,739
I hadn't posted a riddle in many days when a loyal reader called to say that she missed the riddles. She enjoys the challenge of solving puzzles and riddles. So, as long as I have just one reader who enjoys the daily riddles, I will continue to publish them.
This riddle is dedicated to our good friend, Sharon. And it's a really tough one! The solution to it is very ingenious! Sharon, if you solve it, let me know!
"Bags and Beads"
You are given 5 bags. There are 10 beads in each of the bags. In four of the bags, the beads each weigh 10 grams. In the remaining bag, each bead weighs only 9 grams. All the bags and beads look identical. You must find out which bag has the lighter beads. The problem is that all the bags look identical and all the beads look identical. You can use a scale, but it has to be a single-tray scale, not a two-tray balance scale. Also, you may use the scale only once. How can you find out which bag has the lighter beads?
(For Solution see Comment Section.)
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SOLUTION FOR BAGS AND BEADS:
ReplyDeleteLabel the bags from 1 to 5. 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 and 5. Put these 15 beads on the tray of the scale.
If all 15 weighed 10 grams, the scale would register 150 grams. But since one or more of the beads weighs only 9 grams, the scale will register less than 150. Subtract the number on the scale from 150. Your answer will tell you the number of the bag with the lighter beads. (If the scale registers 148, it’s bag #2. If the scale registers 145, it’s bag #5.)