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Planet fourfi resides in 4 dimensional space and thus the currency used by its residents are 3 dimensional objects. The rupee notes are cubical in shape while their coins are spherical, however the coin minting machinery lays out some stipulations on the size of the coins. The diameter of the coins should be at least 256 mm and not exceed 4096 mm. Given a coin, the diameter of the next larger coin is at least 50% greater. The diameter of the coin must always be an integer. You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?

Read Solution (Total 1)

It's given that the diameter of the coins should be at least 256mm and at most 4096mm.
Also, diameter of next larger coin is at least 50% greater(and an integer).

So,
diameter of the 1st coin=256
" " " 2nd " = 256*1.5=384
" " " 3rd " = 384*1.5=576
4th " = 576*1.5=864

Similarly we'll get the following values (256 < dia_value < 4096) for diameters of different coins: 256,384,576,864,1296,1944,2916
Since all are integers all the values are allowed.

So total no. of types of coins possible to be desined= 7.
12 years agoHelpfull: Yes(7) No(0)

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