At the livestock market, the sheep were secured in 36 pens arranged in a 6x6 grid, the number in each pen shown below.
7 5 5 3 6 2
8 1 7 6 5 1
5 8 4 3 4 5
4 6 8 1 2 9
1 2 8 4 7 8
6 5 3 7 4 5
"I want to make a tidy sum out of it," said the farmer. So, in line with the farmer's wishes, the buyer bought all of the sheep in each of 12 pens.
Remove 12 of the 36 numbers to leave four numbers in each row and column, so that each of the six horizontal lines and each of the six vertical lines totals 20.
Answer:
7 0 5 0 6 2
8 1 0 6 5 0
0 8 4 3 0 5
4 6 8 0 2 0
1 0 0 4 7 8
0 5 3 7 0 5
Explanation:
Start by examining the 6 rows.
7+5+5+3+6+2=28 (remove columns 2,4 or 3,4 or 5,6).
8+1+7+6+5+1=28 (remove columns 1,2 or 3,5)
5+8+4+3+4+5=29 (remove columns 1,3 or 1,5 or 3,6 or 5,6)
4+6+8+1+2+9=30 (remove columns 1,2 or 3,5 or 4,6)
1+2+8+4+7+8=30 (remove columns 2,3 or 2,6)
6+5+3+7+4+5=30 (remove columns 1,5 or 2,6 or 3,4)
4 is the least frequently removed column among these choices, so what are the combinations that eliminate 2 entries from column 4 ?
Remove 3,4 from row 1 and 4,6 from row 4 DOESN'T WORK
Remove 2,4 from row 1 and 3,4 from row 6 DOESN'T WORK
Remove 3,4 from row 1 and 3,4 from row 6 DOESN'T WORK
Remove 4,6 from row 4 and 3,4 from row 6 DOESN'T WORK
Remove columns 2,4 from row 1 and 4,6 from row 4
EUREKA !!!!!
7 0 5 0 6 2
8 1 0 6 5 0
0 8 4 3 0 5
4 6 8 0 2 0
1 0 0 4 7 8
0 5 3 7 0 5
|
|
Posted by Penny
on 2004-03-04 09:53:36 |
A methodical approach quickly solves this one
