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Poker

有9張啤牌, 分別為 1 -9 。 A,B,C,D 4人取牌, 每人取2張。現已知A 取的2張牌之和是 10; B取的2張牌之差是1;
C取的2張牌之積是24; D 取的2張牌之商是3。
請說出他們4人各有哪2張牌?剩下的1張又是咩牌?

**** Hidden Message *****

A list of possibilities:
A=(1,9),(2,8),(3,7),(4,6)
B=(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9)
C=(3,8),(4,6)
D=(1,3),(2,6),(3,9)

5 can only be held by B and 7 can only be held by A or B.
Case 1
if B=(4,5) or (5,6) then
C=(3,8) then
D=(2,6) then
B=(4,5)   (B=(5,6) will lead to contradiction becase 6 is replicated)
then
A=(1,9)
the remaining card is 7

Case 2
if B=(6,7) then
C=(3,8) then
D=(2,6) which lead to contradiction because 6 is replicated.

Case 3
if B=(7,8) then
C=(4,6) then
A=(1,9) then
D has no answer

Case 4
if A=(3,7) then
C=(4,6) then
D has no answer

Answer:
A=(1,9)
B=(4,5)
C=(3,8)
D=(2,6)
Remaining card=7

[[i] 本帖最後由 sheungwan 於 2007-5-29 14:09 編輯 [/i]]

A: 1,9
B: 4,5
C: 3,8
D: 2,6
Remaining card is 7

[quote]原帖由 [i]sheungwan[/i] 於 2007-5-28 04:07 發表
A list of possibilities:
A=(1,9),(2,8),(3,7),(4,6)
B=(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9)
C=(3,8),(4,6)
D=(1,3),(2,6),(3,9)

5 can only be held by B and 7 can only be held by A or  ... [/quote]

Thanks for your sharing