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
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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.
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...".
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
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.
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.
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!
To solve this problem, we need to find the sums of the numbers in both the horizontal and vertical circles. Since there are three horizontal and three vertical circles, we need to ensure that the sums of the numbers in each set of circles are equal.
Let's start by finding the sum of the numbers in the vertical circles. Since each of the numbers (7, 8, 9, 10, and 11) can be used only once, the sum of the vertical circles must be:
7 + 8 + 9 + 10 + 11 = 45
Now, let's consider the possible solutions for the horizontal circles. We know that the sum of the numbers in each set of horizontal circles must equal the sum of the numbers in the vertical circles, which is 45.
1. Solution 1:
OOO
7 8 9
10
In this solution, the sum of the numbers in the horizontal circles would be:
7 + 8 + 9 = 2