Ashish is given Rs. 158 in one rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re. 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?
Explanation:
To express any number with the least number of bags of coins, we need these bags of coins to consist of the number of coins as 20, 21, 22, 23, …, and the remaining coins should be put in one bag.
∴ The bags would consist of 1, 2, 4, 8, 16, 32 and 64 coins.
This takes care of 127 coins.
There are 31 coins remaining.
Now, any number, greater than 127 and less than 158, can be expressed as,
n = 158 − k ...(where k is a positive integer less than 31)
As, the present 7 bags are sufficient to count 31 different coins, any number greater than 127 can be counted even if we place remaining 31 coins in a single bag.
∴ Total number of bags = 7 + 1 = 8
Hence, option (d).
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