The Missing Numbers

Problem #79
Deadline to submit the solution: September 30th, 2002

 12 5 6 11 7

Fill in the empty squares with numbers 1 to 12, so that:

1. The sum in each row equals 26.
2. The largest number in each column is equal to the sum of the other two numbers in that same column.
3. Each of the numbers (1 to 12) can appear only once in the table.

Q1. The number in the first row.
Q2. The numbers in the second row.
Q3. The numbers in the third row

Solutions:

Lahiru from USA
Solution:
Q1: 3
Q2: 10, 4, 1
Q3: 2, 8, 9

1. I add 1st row answer is 3 as 12+5+6=23 and 26-23=3
2. Then I knew 8+3=11 on 2nd column.
3. Then I knew the answer to column 4 is 1 as 6+1=7
4. Then what is left is 10, 2, 4, 9
5. Then I mixed and added to get 2 and 3rd row to 26 and each column.
About me: I like to play tag. I love killer whales.

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Syed from USA
Solution:
Q1: 12,3,5,6
Q2: 10,11,4,1
Q3: 2,8,9,7

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Unknown from ?
Solution:
Q1: 3
Q2: 10 4 1
Q3: 2 8 9

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Chitta from U.S.A.
Solution:
Q1: 3
Q2: 10,4,1
Q3: 2,8,9

First I found the answer for the first row to make the sum equals 26. Then I filled the first column as I can't chose any number bigger than 12. Then I crossed the numbers which I used and finally got the answer after 3, 4 attempts.
About me: I like to eat icecream and I like doing Math. And I liked this math challenge. I like to play with cars.

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Sushant from USA
Solution:
Q1: 3
Q2: 10,4,1
Q3: 2,8,9

My strategy was to add numbers up to 26.
About me: I like to play sports with my friends at school.
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 12 3 5 6 10 11 4 1 2 8 9 7

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