There arc 11 bags of coins 11 coins per bag Coins arc size c

There arc 11 bags of coins. 11 coins per bag. Coins arc size, color, etc. cxecpt weight. 10 bags contain gold coins cach coin weighing 11 grams (so the weight of each bag of gold coins is 121 grams). However, the coins in the remaining bag are counterfeit and weigh either 10 grams or 12 grams, i.e. each coin may be 1 gram lighter or heavier (so the weight of the bag of counterfeit may be 110 or 132 grams). Using a scale (which reads the weight in gram) only one time, find the bag of counterfeit coins.

Solution

Step 1: we name all the bag of gold coins as 1, 2, 3......8, 9, 10 and 11

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, 10 coins from bag 10 and 11 coins from bag 11 onto the scale. Find out the total weight.

Step 3: the total weight should have been 11 grams X (1+2+3+4+5+6+7+8+9+10+11=66) = 726grams if all coins are the same (11grams 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.

Hence, the counterfeit coins bag can be found.