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.
Of the three possible solutions, which numbers can be used in the middle circle of the horizontal row? Show each of the resulting solutions.
So the numbers are 7,8,9,10 and 11. There are three horizontal circles and three verticle circles.
OOO
O
O
I asked this question a few days ago, I still didn't understand, but the person helping me already left before responding again.
Here's your original question and answer.
http://www.jiskha.com/display.cgi?id=1255971637
Perhaps a math teacher can explain it to you. Also -- do your circles look more like this?
O O O
. O
. O
Yes, they look like that. Does that change the sequence?
The verticle circles are below the middle horizontal circle.
7 11 10 7+11+10=11+9+8=28
9
8
8 9 10 8+9+10=9+7+11=28
7
11
8 7 11 8+7+11=7+9+10=26
9
10
of the three possible solutions
only 7, 9, and 11 will work in
the center horizontal row.
To find the solution to this problem, we need to consider the sum of the numbers in each set of circles. In this case, we have three horizontal circles and three vertical circles.
Step 1: Determine the sum of the numbers in each set of circles.
For the horizontal circles, let's represent them as:
(A) + (B) + (C) = Sum1
For the vertical circles, let's represent them as:
(D) + (E) + (F) = Sum2
Step 2: Set up an equation.
Since the sum of the numbers in both sets of circles should be equal, we can set up the equation:
Sum1 = Sum2
Step 3: Assign numbers to the circles.
Assign the numbers 7, 8, 9, 10, and 11 to each of the circles, ensuring no number is repeated. Let's start with the horizontal circles:
(A) + (B) + (C) = Sum1
Now, let's consider the vertical circles:
(D) + (E) + (F) = Sum1
Step 4: Look for solutions.
Since there are only three horizontal circles, we can manually calculate all possible combinations to see which ones satisfy the equation. Let's assess the options:
Option 1: 7 + 8 + 9 = 24
In this case, we need to find numbers that sum up to 24 for the vertical circles. However, the remaining numbers (10 and 11) cannot be combined to achieve 24, so this option does not work.
Option 2: 7 + 8 + 10 = 25
In this case, Sum1 = 25. Now we need to find numbers that sum up to 25 for the vertical circles. The remaining numbers (9 and 11) combine to form 20, leaving a difference of 5. As there is no number 5 available, this option does not work.
Option 3: 7 + 8 + 11 = 26
In this case, Sum1 = 26. Now we need to find numbers that sum up to 26 for the vertical circles. The remaining numbers (9 and 10) combine to form 19, leaving a difference of 7. We have number 7 available, so this option works.
(D) + (E) + (F) = 7 + 9 + 10 = 26
Therefore, the only solution that works for the given numbers is:
OOO
78O
O9O
In this solution, you can see that the numbers 7, 8, and 11 are used in the horizontal circles, and the middle circle of the horizontal row is filled with the number 10.