 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Magic Sum (Posted on 2005-09-22) Someone fills a 6x6 matrix with the numbers from 1 to 36 first across, then down, like:
``` 1  2  3  4  5  6
7  8  9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
```
Now they ask for volunteers to randomly select numbers. The number selected will be circled and the others in the same row and column will be crossed out. Non-crossed out numbers are selected until no more numbers can be chosen. For example, selecting 8 means that 7, 9, 10, 11, 12, 2, 14, 20, 26, and 32, can no longer be chosen.

When all is said and done, the total of the circled numbers is 111.

Can you prove why this is so?

To give credit where due, I first saw this on curiousmath.com

 See The Solution Submitted by Bob Smith Rating: 3.0000 (4 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solution | Comment 2 of 6 | ` `
`An element of the array is A(I,J) = 6(I-1)+J.`
`There is only one circled element in each rowand column. Summing the element in each row:`
`  Row  Element`
`   1     0 + J_1 +`
`   2     6 + J_2 +`
`   3    12 + J_3 +`
`   4    18 + J_4 +`
`   5    24 + J_5 +`
`   6    30 + J_6 `
`     =  90 + (J_1 + J_2 + J_3 + J_4 + J_5 + J_6)`
`     =  90 + 21`
`     =  111      `
`  `

 Posted by Bractals on 2005-09-22 02:57:49 Please log in:

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