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Topic: What An Odd Set Of I (Read 995 times) |
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K Sengupta
Senior Riddler
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What An Odd Set Of I
« on: Dec 11th, 2005, 11:02pm » |
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Let S be the set of all odd integers greater than one. For each x c S ( belonging to S ) let us denote by d(x) the unique integer satisfying the undernoted inequality:
2d(x) < x < 2d(x) + 1
For both A ,B c S, define
A # B = 2d(A) -1 *(B-3) + A ;
For example, to calculate 5 # 7, note that
22 < 5 < 23. So, d(5) =2 giving, 5 # 7 =22-1* (7-3) + 5 = 13.
PROVE that if A,B,C c S;
(I) A # B c S and,
(II) (A # B) # C = A # ( B # C);
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| « Last Edit: Dec 12th, 2005, 4:31pm by Icarus » |
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Icarus
wu::riddles Moderator
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Boldly going where even angels fear to tread.
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Re: What An Odd Set Of &nb
« Reply #1 on: Dec 12th, 2005, 4:33pm » |
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Pardon my edit, but I think this is easier to follow than using "E" as an element sign in the midst of other capital letters used as variables.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Grimbal
wu::riddles Moderator
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Re: What An Odd Set Of &am
« Reply #2 on: Dec 13th, 2005, 2:14am » |
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Isn't ( more readable than c?
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Joe Fendel
Junior Member
Posts: 68
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Re: What An Odd Set Of I
« Reply #3 on: Dec 13th, 2005, 1:02pm » |
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It looks to me like (I) is trivial (since an even number plus an odd one is an odd number), and (II) simplifies to proving that
d(A # B) + 1 = d(A) + d(B)
for all odd A, B > 1.
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Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
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Posts: 4863
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Re: What An Odd Set Of &am
« Reply #4 on: Dec 13th, 2005, 3:03pm » |
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on Dec 13th, 2005, 2:14am, Grimbal wrote:Isn't ( more readable than c? |
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I hadn't thought of that. (I really wish we could have our mathematical beastiary back!  )
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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