HANGOVER - Hangover

How far can you make a stack of cards overhang a table? If you have one card, you can create a maximum overhang of half a card length. (We're assuming that the cards must be perpendicular to the table.) With two cards you can make the top card overhang the bottom one by half a card length, and the bottom one overhang the table by a third of a card length, for a total maximum overhang of 1/2 + 1/3 = 5/6 card lengths. In general you can make n cards overhang by 1/2 + 1/3 + 1/4 + ... + 1/(n + 1) card lengths, where the top card overhangs the second by 1/2, the second overhangs tha third by 1/3, the third overhangs the fourth by 1/4, etc., and the bottom card overhangs the table by 1/(n + 1). This is illustrated in the figure below.


The input consists of one or more test cases, followed by a line containing the number 0.00 that signals the end of the input. Each test case is a single line containing a positive floating-point number c whose value is at least 0.01 and at most 5.20; c will contain exactly three digits.


For each test case, output the minimum number of cards necessary to achieve an overhang of at least c card lengths. Use the exact output format shown in the examples.


3 card(s)
61 card(s)
1 card(s)
273 card(s)

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gulbarga master: 2015-02-17 06:47:42

very poorly worded problem statement for a very simple piece

John Doe: 2015-02-12 12:08:59

Daniel, I'm not disputing that you can get AC with the given formula.
I'm saying that if you try a real-life experiment with two cards you will get a maximum overhang of 1/2 + 1/4 = 3/4, not 1/2 + 1/3 = 5/6 as stated.

Daniel Carvalho: 2015-02-12 02:20:45

Extremelly easy, but bad formulated. John Doe, your formulation is wrong. Use the given general formula.

John Doe: 2015-02-11 16:43:04

Does the problem specification reflect reality?
It seems to me that the correct overhang equation is
1/2 * (1 + 1/2 + 1/3 + ... + 1/n)
and you cannot get 1.00 with only three cards.
Excuse my nitpicking :)

D: 2015-02-07 17:02:59

can't see the image.

(Francky) ⇒ Updated ; image visible.

Last edit: 2015-02-07 21:06:49
shreya goyal: 2015-02-05 21:39:15


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