Cut the chain | 12 Sep 2009
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Go4Expert Founder
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| 12Sep2009,18:53 | #1 |
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A Man has 23-link chain. He lives in a house whose rent is worth one link for one day. What is the fewest number of cuts he can make in the chain for paying rent for each day.
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~ Б0ЯИ Τ0 С0δЭ ~
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| 12Sep2009,19:47 | #2 |
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2 cuts.
He would cut link no. 4 and 11. ( counting from the same end ) 
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~ Б0ЯИ Τ0 С0δЭ ~
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| 12Sep2009,19:59 | #3 |
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Explanation ::
After cutting links 4 and 11, he would be left with : (A) Two chains of 1-link length each : link 4 and link 11. (B) One chain of 3-link length : link 1~3 (C) One chain of 6-link length : link 5~10 (D) One chain of 12-link length : link 12~23 He then pays the 2 chains in (A) for the first 2 days. On day 3, he gets back the 2 chains and gives (B) chain as rent. Then pays 2 (A) chains for next two days. And gets back 2 (A) chains + the (B) chain on day 6 and gives (C) chain as rent. Then pays the 2 (A) chains and the (B) chain as rent for next 5 days. And gets back all chains and pays the (D) chain as rent. Then, he repeats the above steps till day 23.
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Go4Expert Founder
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| 13Sep2009,11:19 | #4 |
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Quote:
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~ Б0ЯИ Τ0 С0δЭ ~
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| 13Sep2009,18:10 | #5 |
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Of course he could have, and so there is no point of all this.
So, obviously I meant that only (one link/day), just I am lazy to type  OK. Let's have it your way : Explanation :: After cutting links 4 and 11, he would be left with : (A) Two chains of 1-link length each : link 4 and link 11. (B) One chain of 3-link length : link 1~3 (C) One chain of 6-link length : link 5~10 (D) One chain of 12-link length : link 12~23 He then pays the 2 chains in (A) for the first 2 days (one chain on each day). On day 3, he gets back the 2 chains and gives (B) chain as rent. Then pays 2 (A) chains for next two days (one chain on each day). And gets back 2 (A) chains + the (B) chain on day 6 and gives (C) chain as rent. Then pays the 2 (A) chains (one chain on each day) for day 7 and 8. On day 9, he pays (B) chain as rent and gets back the 2 (A) chains. He then pays the 2 (A) chains (one chain on each day) for next 2 days (till day 11). And gets back all chains and pays the (D) chain as rent on day 12. Then, he repeats the above steps till day 23. Phew... > 100 chars added. |
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Go4Expert Founder
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| 13Sep2009,18:52 | #6 |
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OK Got it.
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Banned
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| 15Sep2009,14:13 | #7 |
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Congrs SP
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~ Б0ЯИ Τ0 С0δЭ ~
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| 15Sep2009,17:56 | #8 |
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Thanx naimish
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Banned
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| 16Sep2009,08:12 | #9 |
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 SP 
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