One to One Hundred

99 unique numbers between 1 and 100 are listed one by one, with 5 seconds pause between every two consecutive numbers. If you are not allowed to take any notes, what is the best way to figure out which is the missing number?

SOLUTION

Keep up adding the given numbers and remember only the last two digits of the sum. In the end, if the result is less than 50, subtract it from 50. If the result is larger than 50, subtract it from 150. This method works because the sum of all numbers from 1 to 100 is 5050, so if you know the sum of all the listed numbers, you will know the missing number as well.

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