Simple Arrangement
Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, second row of two balls and so on. If 669 more balls are added then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each of the triangle did have. Find the initial number of Balls.
The answer is 1540.
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1 solution
1+2+3+.....+x=Y --> Total number of balls in triangle --(i) Y+669=(x-8)(x-8) --> Total number of balls in square ---(ii)
from eq (i) Y=x(x+1)/2 --(iii)
from eq (ii) and (iii) x(x+1)/2+669=(x-8)(x-8) => x=55
Initial number of balls = Y = x(x+1)/2 = 55*56/2 = 1540