Interview Question

Given a chess board of N * N, we have to put only rooks on chess board we wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:
 Each square of the board contains at most one rook.
 There are no four rooks forming a rectangle.
 Formally, there should not be any four valid integers r1,c1, r2, c2 (r1â‰ r2,c1â‰ c2) such that there are rooks on squares (r1,c1), (r1,c2), (r2,c1) and (r2,c2)
 The number of rooks is at least 8N
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A killer bee was buzzing, a queen bee was buzzing, a worker bee was buzzing, and a honey bee was buzzing.
How many bees were in buzzing ?
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While enjoying a giddy ride at the carousel Sammy propounded a puzzle which reflects much credit to his mental abilities.
“One third of the number of kids riding ahead of me, added to threequarter of those riding behind me gives the correct number of children on this MerryGoRound” is the way he puts it; but it will puzzle you quite a little to tell just how many riders there were at this whirling circus.View SolutionSubmit Solution 721 views
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Consider a list of 2000 statements:
1) Exactly one statement on this list is false.
2) Exactly two statements on this list are false.
3) Exactly three statements on this list are false.
. . .
2000) Exactly 2000 statements on this list are false.
Which statements are true and which are false?What happens if you replace “exactly” with “at least”?
What happens if you replace “exactly” with “at most”?
What happens in all three cases if you replace “false” with “true”?
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You have five pieces of chain, each consisting of three links. You want to make one long chain of these five pieces. Breaking open a link costs 1 $, and welding an open link costs 3 $.
Is it possible to make one long chain of the five pieces, if you have just 15 $?
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A boat of mass M1 is floating in a lake of water. The volume of the lake is V. The water surface is initially at height h, as measured relative to the lake’s floor. There is an anchor of mass M2 sitting on the boat’s deck. A person standing on deck picks up the anchor and throws it overboard. The anchor then sinks to the bottom of the lake, and the water surface height becomes h’.
Which of the following qualitative relationships is correct? What assumptions are you making about the values of M1, M2, h, and V?
h’ h
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A specialist Gardener asked by a Mathematics professor to plant four trees that are all equidistant from each other. How do he place the trees?
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Pairs of primes numbers separated by a single number are called prime pairs like 17 and 19. Prove that the number between a prime pair is always divisible by 6 (assuming both numbers in the pair are greater than 6).
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A snail is at the bottom of a well that is 20 meters in depth. Every day the snail climbs 5 meters upwards, but at night it slides 4 meters back downwards. How many days must elapse till the snail reaches the top of the well?
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