Adding numbers
Probability
Level
2
There are 40 numbers on the blackboard from 1 to 40.we are selecting the two numbers a,b randomly and placing a new number a + b - 1 on deleting both numbers a and b.Find the last number left on the blackboard.
820
781
789
782
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This is quite easy. Forget the question. Assume the numbers are a, b, c, d. Now, at first you'll get (a+b-1),c,d. Then you'll get {(a+b-1)+c-1},d. Then you'll get [{(a+b-1)+c-1}+d-1}]. Now observe this. You can realize that it's nothing but some less than the summation of all given numbers. How less? It's 1 when you add 2 numbers. 2 when you add 3 numbers. so it's 39 when you add 40 numbers. So 1+2+3...+40= 40*41/2=820. And the answer is 820-39=781.