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Question:
There are 4 buckets of coins. Real coins weigh one gram each. fake coin weigh 2 grams each. Each bucket is fake (contains only fake coins) or real (contains only real coins).
You have weighing machine(not balance), which can be used for only one weighing. If there are 9 coins per bucket, how can you determine all the buckets that are fake with just one weighing.
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Answer:
If it has only one or zero fake buckets then
Take 1 coin from 1st bucket , 2 coins from second bucket , 3 coins from 3rd bucket and 4 coins from 4th bucket.
If no bucket has fake coin then the weight will be 10 gram.
If 1st bucket has fake coins then the weight will be 11grams.
If 2nd bucket has fake coin then the weight will be 12 grams.
If 3rd bucket has fake coin then the weight will be 13 grams.
If 4th bucket has fake coin then the weight will be 14 grams.
Based on the weight we can find the which one is fake one.
If there are more fake buckets then follow the below strategy
One Coin from 1st bucket, 2 coins from second bucket, 4 coins from 3rd bucket, 8 coins from 4th bucket.
Now if total weight is 15 grams then no fake bucket.
If total weight is more than 15 gram. then (Total weight - 15) is:
1 means first bucket
2 means second bucket
3 means first and second ( Sum of 1st and 2nd )
4 means only 3rd bucket
5 means 3rd and 1st bucket ( Sum of 1st and 3rd )
6 means 2nd and 3rd bucket ( sum of 2nd and 3rd )
7 means 1st, 2nd and 3rd bucket ( sum of 1st , 2nd and 3rd )
like that .. till
30 means all buckets are fake ones.
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