help!! 數學邏輯推理題 in English

[匿名]

2010-12-16 2:32 am

Please help to answer the below!!!!! Please give steps / explain!!! Explain in Chinese is also ok!!

Adam, Ben, Carl, David and Edward join a basketball competition. Each of them has 10 shots and 1 point is given to each successful shot. They are asked for their results after the competition. The following is their replies: Adam : “No two of us get the same point.” Ben : “The total point of A and I is equal to that of the other three.” Carl : “The total point of D and I is less than that of the other three by 3.” David: “No one gets less than 2 points.” Edward: “If our points are multiplied, the last 2 digits of the result would be 50.”
It is found that one of them told a lie. What are their total points?

回答 (1)

用戶2053

2010-12-16 3:46 am

✔ 最佳答案

Ben : A + B = C + D + E
Carl : C + D = A + B + E - 3Sub Carl into Ben :A + B = (A + B + E - 3) + E2E - 3 = 0E = 1.5 (Contradiction)Therefore either Ben or Carl told a lie.By Adam , none of them get the same poin is true.By David , the possible points of five people are :2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10.By Edward , the last 2 digits of ABCDE is 50.We know ABCDE is divisible by 50 = 5 x 10So two of them got 5 and 10 points. And no people get even points i.e. 2 , 4 , 6 , 8 points otherwise the last 2 digits is 00 .(Contradiction)Hence the other 3 peoples got 3 , 7 , 9 points.Their total points = 5 + 10 + 3 + 7 + 9 = 34.

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