### Number 214 of a series

Here is a calendar. It could be any calendar. I drew a 3×3 box around 9 dates. What is the sum of the numbers in the box? You are allowed five seconds.

Post your answer in the comments section below.

## Update and Solution

Mike has the right approach. To solve this in under five seconds you need to know about the life of Carl Friedrich Gauss. As a young school boy he was assigned the problem of adding up a column of large numbers. He noticed the professor wrote the column of numbers as an arithmetic series. He quickly realized the sum was the product of the average and the number of numbers. The average would be the middle number (odd number of numbers) or half way between the two middle numbers. He turned in his answer so quickly the professor was astounded.

Days in a month are an arithmetic sequence. All this problem does is to chop the sequence into three , equally spaced, sequences of the same length. The sum will be 9 times the middle number.

180 (in under 5 seconds)

If x is the sum of the top row of the box, then the second row sum is x+3*7 and the third row is x+3*14. That makes for a total of 3x + 3*21. The formula should work for any box with all 3 of its rows in the same month. For this box, x = 12 + 13 + 14. I’ll leave it to the student to do the arithmetic and get the final answer.

Elmo’s answer takes more than 5 seconds. 5 seconds answer: 9 times the middle number.

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