P & C (Chess)

JEE Advanced Preparation › Algebra questions › P & C (Chess)

17 ants are roaming over the chess board of the area 8 X 8 (I.e is 64 square inches) then atleast two of them must always be closer than
(a) 2 inches (b) 2 âˆš2 inches (c) âˆš2 inches (d) none of these

#Mathematics #Algebra

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7 Answers

62

Lokesh Verma ·2009-11-18 10:04:21

divide the chess board into 16 parts.. each part a square of size 4

so by PHP, there is one of these 2x2 squares having atleast 2 ants.

The max distance between these will be 2âˆš2

Hence the seperation will be less than 2âˆš2

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11

Tush Watts ·2009-11-18 10:09:20

oh yeah
got it thanx a lot sir [1]

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Bicchuram Aveek ·2009-11-18 10:18:00

@Nishant Sir

Why aren't they 1X1 squares but 2X2 ?????

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Tush Watts ·2009-11-18 10:21:04

@ Aveek
I guess bcoz of Pigeon hole principle (PHP)

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Bicchuram Aveek ·2009-11-18 10:28:28

oooo yesss got it !!! Nishant Sir has done it very well !!!!!

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rahuliit ·2009-11-18 22:08:10

whats that pegion hole principle sir

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24

eureka123 ·2009-11-18 22:12:05

http://en.wikipedia.org/wiki/Pigeonhole_principle

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Your Answer

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