Question
The integers 1,2,.........64 are written on a blackboard. The following operation is repeated 63 times: Any 2 numbers are chosen out of these 64 numbers and replaced with a number equal to 1 minus the sum of 2 numbers. What will be the number left over on the board after 63 operations?
Answer: Option A
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A
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Option (a)
They key here is any number, so basically choose the easiest pair of numbers and solve the question. My choice will be the numbers distanced equally from the middle value such as 1 & 64, 2 & 63 etc. All of them will be replaced by 64. So after the 1st32 operations, you have 32 64s left. The pattern will look like this:-
After 32 → 32 64s
After 16 more → 16 127s
After 8 more → 8 253s
After 4 more → 4 505s
After 2 more →2 1009s
After 1 more →1 2017
Total number of operations = 32 + 16 + 8 + 4 + 2 + 1 = 63
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