# What is the number?

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There is a 5 digit number. With a 1 after it, it is three times as large as it would be with a one before it.

What is the number?

posted Sep 12, 2014

3 x 142857 = 428571

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+1 vote

Soham works at a soft drink company and was arranging some particular number of cylindrical aluminium soft drink cans in a square box but the box became full and there were 8 cans remaining to be put in.
Then, he started arranging all cans in a rectangular box where he could arrange 6 cans more along the length than the breadth after putting all the cans in the rectangular box.
He found out that there was still space left for another 11 cans.
What is the number of cans Soham had if it is known that the number of cans were more than 15 and no can was put on top of another can?

A certain number is divided by five, seven is added and the result is quadrupled to get a number 15 higher than the original number.
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I have a puzzle consisting of 100 (10x10) pieces.

What is the minimum number of pieces I have to draw randomly from a pile to be guaranteed that I can join them all together so that no piece is isolated (i.e. not joined to any other piece)?

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Every piece is equally likely to be picked. I don't look whether the first piece has a straight edge or similar tricks.
Every piece only fits together with its neighboring pieces, and there is a unique solution to the puzzle.
Two pieces that only share a corner are not considered "joined."