Question

The integers 1, 2, . . ., 40 are written on a black board. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased, and a new number a + b - 1 is written. What will be the number left on the board at the ends?

• A. 820
• B. 821
• C. 781
• D. 780

Answer 1

The correct option is C 781

Let S = 1 + 2 + . . . + 40.
So, 1 + 2 + a + b + . . . + 40 = S
After 1st step:
1 + 2 + . . . + (a + b - 1) + . . . + 40 = S - 1
So, after each step, the total reduces by 1. Continuing this way after 39 steps, numbers S - 39 = $\frac{40\times 41}{2}-39=781$
Hence, option (c) is the answer.