Question

In a stack of coins, each row has exactly one coin less
than the row below. If we have nine coins, two such
towers are possible. Of these, the tower on the left is the
tallest. If you have 2015 coins, the height of the tallest
tower is.....​

Answer 1

Given : a stack of coins, each row has exactly one coin less  than the row below. nine coins, two such  towers are possible.

To find :  Tallest tower  with 2015 coins

Step-by-step explanation:

There will be maximum number of rows if number of coins at top is least or 1

=> Tallest tower

Let say number of coins at top row = 1

and number of rows = n  

then number of coins at  bottom row  = n

Total number of coins = (n/2) ( n + 1)

=n(n + 1)/2

n(n + 1)/2    = 2015

=> n( n +  1)  = 4030

63 * 64 = 4032

=> n = 63

Total coins would be 63 * 32 = 2016

but coins are  2015

hence top row of single coin will not be there

hence  number of rows = 62

top row = 2   , bottom row  = 63

number of rows = 62  for tallest tower

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