Answer:
R = 13
Explanation:
You have a graphic relating numbers represented by the variables N, R, I, C, H, and you want to know the value of R.
Solution
Adding all of the numbers, we get ...
1 +3 +4 +5 +7 +N +R +I +C +H = 20 +9 +10 +11 +12 +13 = 75
If we add all of the lines, the sum will be twice this value, which means ...
5 × line total = 2×75
line total = 30 . . . . . . . . divide by 5
Going around the center loop clockwise from R, we can write equations for I and C in terms of R:
I = 30 -(6 +R) = 24 -R
C = 30 -(10 +I) = 20 -(24 -R)
C = R -4
At this point, we refer to the list of possible values of the variables, and we see there are only two on the list that differ by 4:
9 = 13 -4
This tells us C = 9 and R = 13.
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Additional comment
The value of I is 24 -13 = 11. The values of N and H can be found to be ...
N = 10, H = 12