Interview Puzzle

How many cases do you need if you have to pack 112 pairs of shoes into cases that each hold 28 shoes?
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A person was prescribed to take two pills (tablets), one each, from the two bottles viz. Bottle A and Bottle B, daily. The tablets are exactly look alike.
The medicines have to be taken exactly one tablet from each bottle, neither less nor more, else the medicines will not be effective.
One fine day, the patient popped out one tablet from Bottle A, but while taking the tablet from bottle B, by mistake, two tablets spilled over. Now he has three tablets in his hand, and he can’t put back the extra tablet to Bottle B as all the tablets are identical in looks.
He has to ensure that he takes exactly one tablet from each of the bottles and at the same time he must avoid any wastage of the medicine. What He will do?
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Given six distinct colors, in how many unique ways can a sixfaced cube be painted such that no two faces have the same color?
Note: The mixing of colors is not allowed.
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At a party, four people played a game. Three of them sat one behind the other, so that Abe saw Bill and Cal, and Bill only saw Cal, who sat in front and saw nobody else.
Dave had 5 hats which he showed to his three friends. Three of the hats were blue and two were red.
Now Dave placed a hat on the head of each of his three friends, putting aside the remaining two hats.
Then he asked Abe what color his hat was.
Abe said he couldn’t tell.
Bill was asked the color of his own hat, but he didn’t know for certain either.
Cal, though he couldn’t see any hat at all, gave the right answer when asked what color his hat was.
Do you know what color Cal’s hat was and how he reasoned to find out the correct answer?
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