As shown in the figure, five circles cross and have nine parts.
Number from 1 to 9 are in the nine parts one by one.
The sum of numbers in each circle becomes all 11.
(1) Find the sum of four numbers in P, Q, R and S.
(2) Find numbers in nine parts.
Noted that the number in Q is smaller than the number in R.
Answer
(1) 10
(2) A 8, B 7, C 6, D 5, E 9, P 3, Q 1, R 4, S 2
Solution
(1) Total from 1 to 9 is 45.
All totals in the table below are 11 × 5 = 55.
Accordingly P + Q + R + S = 55 - 45 =10.
(2) Because 10 = 1 + 2 + 3 + 4, P, Q, R, S are numbers of 1 ~ 4.
A ~ E are numbers of 5 ~ 9.
Because 11 = 9 + 2 = 8 + 3 = 7 + 4, it's considered in case of the following 6 ways of the table.
① Q = 1, R = 4, then B = 8 which is not applicable.
② Q = 1, R = 3, then C = 7 which is not applicable.
③ Q = 1, R = 4, then B = 7, C = 6, and D = 5 which is applicable.
④ Q = 1, R = 2, then B = 7 which is not applicable.
⑤ Q = 1, R = 3, then C = 7 which is not applicable.
⑥ Q = 1, R = 2, then C = 8 which is not applicable.
According to ① ~ ⑥, only the case of ③ can be applied.
