Posted by Kelly on Monday, October 19, 2009 at 1:00pm.
Use each of the numbers 7, 8, 9, 10, and 11 once and only once to fill in the circles so that the sum of the numbers in the three horizontal circles equals the sum of the numbers in the three vertical circles.
OOO
O
0
Of the three possible solutions, which numbers can be used in the middle circle of the horizontal row? Show each of the resulting solutions.

Math  tchrwill, Monday, October 19, 2009 at 2:15pm
If there are 3 vertical, and 3 horizontal, circles to be filled in using a set of given numbers only once, you would need 9 numbers.
For instance,
8..1..6
3..5..7
4..9..2
Can you clarify your problem statement of "...using each of the numbers once and only once...".

Math  Kelly, Monday, October 19, 2009 at 2:37pm
No, I am not sure.
The exact diagram looks like this
O O O
O
O
The circles are to be filled in with the numbers given.
The possible multiple choice answers given are:
A) 7, 8, and 9 B) 7, 9, and 11
C) 9, 10, and 11 D) 8, 9, and 10

Math  tchrwill, Monday, October 19, 2009 at 4:02pm
I think I see what you are driving at now.
9.8.10
7
11
9.10.8
7
11
9.8.10
11
7
9.10.11
11
7
7.8.11
9
10 and the same variations as shown above.
11.7.10
8
9 and the variations.

Math  Kelly, Tuesday, October 20, 2009 at 11:48am
I still don't understand?
Also the two verticle circles are actually under the second horizontal circle, not the first. For some reason it didn't post like that.
(I don't know if that makes a difference or not)
What I don't think I understand are the purpose of the circles, or maybe it is the purpose of the placement of the numbers (which is really the same thing)
I am sorry I am not grasping this.

Math  Bell, Wednesday, October 21, 2009 at 6:03pm
The circles are just there to show us where they want the numbers. 3 across and 3 down in the middle. Both numbers across and down the middle must equal the same number.
Follow tchrwill's examples and you will find it!
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