16 factory workers made 40 pieces in a certain amount of time. how many workers are needed to make (1) 20, (2)25 and (3)100 pieces in the same amount of time, assuming each worker works at the same rate?

1. 40 units___16 workers

20 units___x= 8 workers

(20*16)/40=8

2. 40 units___16 workers

25 units___x= 10 workers

(25*16)/40=10

3. 40 units___16 workers

100 units___x= 40 workers

(100*16)/40=40

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18