Each of the two boys (Alex and Marvin) and three girls (Candy, Ellen and Venus) scored a
different grade in a recent Mathematics test. The students made the following observations on
their results (namely, A, B, C, D and E, A being the best and E being the worst):
(O1) Alex did better than two or more of the girls;
(O2) The worst grade was not scored by a girl;
(O3) Venus did not score an A;
(O4) Candy scored a C
[Note: In answering the following questions, you may like to make use of the
following
A_____________
B_____________
C_____________
D_____________
E_____________
template, with student name(s) or initial(s) on each scoring line.]
(a)(i) If Alex did not score an A, what were the grades scored by Alex, Ellen and Venus?Explain Briefly.
(a)(ii)If a boy scored an A, who was this boy? What were the possible grades scored by
Ellen and Venus? Explain Briefly.
(a)(iii)If all the girls did better than the boys, which of the four observations must be
incorrect?Explain briefly.
(b)Catherine and Christine take turns breaking a piece of chocolate consisting 5 x 10
small square pieces. At each turn, they may only break along the division lines of the small square pieces and it is agreed that Catherine will start the breaking first.
(i) If they keep breaking the pieces up until only the small square pieces remain and no
more breaking up is possible, who will win the game? Explain briefly.
(ii) If the winner is the one who first obtains a single piece of the small square pieces, who
will win the game and what will be her winning strategy?
How to calculate this question
2014-11-07 6:51 am
回答 (2)
2014-11-08 5:11 pm
✔ 最佳答案
From O1, O2, we know that Marvin was the worst, he scored E, and Alex might scored A or B as he did better than 2 or more of the girls.From O4, we know that Candy scored C, and from O3, we know that Venus did not score A.According to the above hints, the arrangement (from A to E) is：?, ?, Candy, ?, MarvinTherefore, the possible arrangements may be：(1) Alex, Venus, Candy, Ellen, Marvin(2) Alex, Ellen, Candy, Venus, Marvin(3) Ellen, Alex, Candy, Venus, Marvin(ai) If Alex did not score an A, then, obviously, only case (3) satisfy, that is：Grade A：Ellen, grade B：Alex, grade C：Candy, grade D：Venus, grade E：Marvin
(aii) If a boy scored an A, then, he is Alex. This is the cases (1) or (2), and so, Ellen and Venus might score either grade B or D.
(aiii) If all the girls did better than the boys, then the incorrect one is O2, "Alex did better than two or more of the girls".
(bi) As there are totally 13 lines (4 rows and 9 columns, see below), and Catherine could take the 1st one, so she could also take the 3rd, 5th, 7th, 9th, 11th and the 13th (the last one line), that means she could win the game.〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇一十一十一十一十一十一十一十一十一十一 row 1〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇一十一十一十一十一十一十一十一十一十一 row 2〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇一十一十一十一十一十一十一十一十一十一 row 3〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇一十一十一十一十一十一十一十一十一十一 row 4〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇丨〇 C1 C2 C3 C4 C5 C6 C7 C8 C9
(bii) In this case, Catherine could also win the game, she just broke it to become 5 x 5 on the first round (that is, C5). If Christine then broke it to become n x 5, then Catherine could break it to become n x n afterward. So Catherine can first take the chocolate to become 1 x 1.
2014-11-08 12:21 am
Please refer to previous reply:
https://hk.knowledge.yahoo.com/question/question?qid=7014110300115
Is the answer insufficient to show all necessary calculation?
https://hk.knowledge.yahoo.com/question/question?qid=7014110300115
Is the answer insufficient to show all necessary calculation?
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