Answer from SAP forum

來源: Williamluo 於 2010-01-06 16:09:49 [檔案] [舊帖] [給我悄悄話] 本文已被閱讀：次 (1279 bytes)

本文內容已被 [ Williamluo ] 在 2010-01-08 16:59:54 編輯過。如有問題，請報告版主或論壇管理刪除.

http://forumsa.sdn.sap.com/thread.jspa?messageID=8599950&
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A friend of mine sent me a puzzle from IBM month puzzle:

Present a computation whose result is 5, being a composition of commonly used mathematical functions and field operators (anything from simple addition to hyperbolic arc-tangent functions will do), but using only two constants, both of them 2.
It is too easy to do it using round, floor, or ceiling functions, so we do not allow them.
(http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/January2010.html)

It seems no one has solve it yet. I would like have a try:

LOG(2)=LN(2)/LN(10)

THEN LOG(10)=LN(2)/LOG(2)

THEN EXP(LOG(10))=EXP(LN(2)/LOG(2))

THEN 10=EXP(LN(2)/LOG(2))

THEN 5=EXP(LN(2)/LOG(2))/2

THEN EXP(5)=EXP(EXP(LN(2)/LOG(2))/2)=√(EXP(LN(2)/LOG(2)))

Then the answer is 5=LN(√(EXP(LN(2)/LOG(2))))

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It seems there are lots of junior mathematicians interested in IBM puzzles. But most of those puzzles rely too much on mathematical knowledge and skills, not suitable for people are not junior mathematicians. I perfer to design less scholastic puzzles.