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by shashank.ism » Tue Feb 09, 2010 1:08 pm
A man is going to a car auction. All purchases must be paid for in cash. He goes to the bank and draws out Rs. 25,000. Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15 such that he could count any amount from 1 to 25000 using combinations of some envelopes. Each envelope contains the least number of bills possible of any available currency. (for example, no two tens instead of a twenty). The possible currency denominations are 1,2,5,10, 20, 50 and 100. At the auction he makes a successful bid of Rs. 8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount. How many ones (one rupee notes) did the auctioneer find in the envelopes.

1
2
3
4
None of these
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by harsh.champ » Wed Feb 10, 2010 11:42 pm
shashank.ism wrote:A man is going to a car auction. All purchases must be paid for in cash. He goes to the bank and draws out Rs. 25,000. Since the man does not want to be seen carrying that much money, he places it in 15 envelopes numbered 1 through 15 such that he could count any amount from 1 to 25000 using combinations of some envelopes. Each envelope contains the least number of bills possible of any available currency. (for example, no two tens instead of a twenty). The possible currency denominations are 1,2,5,10, 20, 50 and 100. At the auction he makes a successful bid of Rs. 8322 for a car. He hands the auctioneer envelopes 2, 8, and 14. After opening the envelopes the auctioneer finds exactly the right amount. How many ones (one rupee notes) did the auctioneer find in the envelopes.

1
2
3
4
None of these

Each envelope contains the money equal to the 2 raised to
the envelope number minus 1. The sentence "Each envelope contains the least number of bills possible
of any available US currency" is only to misguide you. This is always possible for any amount !!!

One more thing to notice here is that the man must have placed money in envelopes in such a way
that if he bids for any amount less than $25000, he should be able to pick them in terms of envelopes.

First envelope contains, 20 = $1

Second envelope contains, 21 = $2

Third envelope contains, 22 = $4

Fourth envelope contains, 23 = $8 and so on...

Hence the amount in envelopes are $1, $2, $4, $8, $16, $32,
$64, $128, $256, $512, $1024, $2048,$4096, $8192, $8617.

Last envelope (No. 15) contains only $8617 as total amount
is only $25000.

Now as he bids for $8322 and gives envelope number 2, 8 and
14 which contains $2, $128 and $8192 respectively.

Envelope No 2 conrains one $2 bill

Envelope No 8 conrains one $100 bill, one $20 bill, one $5
bill, one $2 bill and one $1 bill

Envelope No 14 conrains eighty-one $100 bill, one $50 bill,
four $10 bill and one $2 bill

[spoiler]Hence the auctioneer will find one $1 bill in the envelopes.
Hence,the ans. is A.[/spoiler]
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