Math Puzzles Questions

Q:

Puzzle : Sequence of numbers

Sequence of numbers are 1, 11, 21, 1211, 111221. What will be the next one in the above sequence?

Answer

 It is a strange sequence. Each number describes the resemblance of the previous one, except the first one.


11 describes the previous '1' which contains one '1'


21 describes the previous '11' which contains two '1'


1211 describes the previous '21' which contains one '2' and one '1'


111221 describes the previous '1211' which contains one '1', one '2' and two '1'.


So the next sequence will be 312211, that is the previous '111221' contains three '1', two '2' and one '1'.

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Q:

Puzzle : Blueberries and Cups

Maria have some blueberries and some cups. If she put 9 blueberries into each cup she will have two cups left. If she put 6 blueberries into each cup she will have three blueberries left over.

Answer

The number of blueberries is equal to number of cups multiplied by 4 minus one left.


That is :


      B = 9(C - 2) -> (1)


Then the number of blueberries will be equal to the number of cups times three plus one left.


That is :


      B = 6C + 3 -> (2)


Now substitute the 1st and 2nd equations:


      B = 9(C - 2)


      B = 6C + 3


      C = 7, B = 45.


Therefore Blueberries = 45 and cups = 7.

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Q:

Puzzle : Bridge Crossing

Jim, Jeanne, Louis and Anne wants to cross the bridge at night. They have only one torch light with them. Only two can cross the bridge at a time. They need torch light to cross the bridge. Each of them walks at a different speed. Jim needs 1 minute, Jeanne needs 2 minutes, Louis needs 5 minutes and Anne needs 10 minutes. A pair must walk together at the rate of the slower person. How these people can cross the bridge within 17 minutes?

Answer

First Jim and Jeanne walks across the bridge, it takes 2 minutes. 


Jim walks back with the torch light, which takes 1 minute. 


Then Louis and Anne walk on the bridge, which takes 10 minutes.


Jeanne comes back with the torch light, it takes 2 minutes.


Finally Jim and Jeanne walks across the bridge, which takes 2 minutes.


Total = 2 + 1 + 10 + 2 + 2 = 17 minutes

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