Q1.
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?
Q2.
Now you should be able to solve this variation, no problem:
You have 10 bags of gold coins, 10 coins per bag, 10 grams per coin, but one bag of coins weigh only 9 grams per coin (because of low quality). How do you find out which bag contains low quality gold coins? You may use a scale only one time. Thanks to Jason Vuong for this variation!
Q3.
You have 9 marbles: 8 of them weigh 1 ounce each; 1 weighs 1.1 ounce. The 9 marbles are all uniform in size, appearance and shape. You have access to a balance scale containing 2 trays - you may use the balance 2 times. You must determine which of the 9 marbles is the heavier one using the balance only 2 times.
Ans1. Label 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.)
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.)
Ans2.
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.
Ans3.
Place 3 marbles on each tray.
- If the first weighing doesn't balance, remove all the marbles from the lighter side, and place one marble on each tray from the heavier tray. The heavier side is the 1.1 ounce marble, but if they balance, then the marble from the heavier tray from the first weighing that was not weighed in the second weighing is the heavier one(1.1).
- If the marbles balance on the first weighing, remove the marbles from the trays, and place 2 of the remaining marbles not yet weighed on the trays, one on each tray. If one is heavier, it is the heavier marble(1.1), but if they balance, the remaining marble not weighed is the heavier one.
- If the first weighing doesn't balance, remove all the marbles from the lighter side, and place one marble on each tray from the heavier tray. The heavier side is the 1.1 ounce marble, but if they balance, then the marble from the heavier tray from the first weighing that was not weighed in the second weighing is the heavier one(1.1).
- If the marbles balance on the first weighing, remove the marbles from the trays, and place 2 of the remaining marbles not yet weighed on the trays, one on each tray. If one is heavier, it is the heavier marble(1.1), but if they balance, the remaining marble not weighed is the heavier one.
0 Response to "Misc Puzzles 1"
Post a Comment