What are the three consecutive numbers that we should start with to get 100 on the top ?
Let three consecutive number in the bottom row be x, x + 1 and x + 2.
Adding adjacent cells in the bottom row, we get
x + (x+1) = 2x + 1 …………………..(1)
Similarly,
(x + 1) + (x + 2) = 2x + 3 ……………………(2)
Adding (1) and (2) for the top most cell, we get
(2x+1) + (2x +3) = 4x + 4
Now we know that 4x + 4 = 100.
⇒ 4x = 100 - 4
⇒ 4x = 96
⇒ x = 96 ÷ 4 = 24
⇒ x + 1 = 24 + 1 = 25
⇒ x + 2 = 24 + 2 = 26
Thus, the three consecutive numbers are 24, 25 and 26.