SOLUTION: A child wishes to build up a triangular piles of toy bricks so as to have one brick In the top flow, 2 in the second, 3 in the third and so on . if he has 100 bricks, how many rows

A triangular pile with n rows of bricks requires  1 + 2 + 3 + . . . + n =  bricks  (= the sum of the first n natural numbers).


The table is


n  (rows)    1   2   3    4     5     6     7     8     9    10    11   12   13

N (bricks)   1   3   6   10    15    21    28     36   45    55    66   78   91


So, having 100 bricks, the child can build 13-stores pyramid.


He (or she) will use 91 bricks, and 100-91 = 9  bricks will left.