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        riddles >> putnam exam (pure math) >> Square Root, Floor, and Factorial
        
(Message started by: THUDandBLUNDER on Jan 5^th, 2007, 10:00am)

Title: Square Root, Floor, and Factorial
Post by THUDandBLUNDER on Jan 5^th, 2007, 10:00am

Express the numbers 4 to 9 as economically as possible using only one '3' and as many square root, floor, and (standard) factorial functions as you require. eg,
1 requires 2 operations as 1 = floor(sqrt(3)) or FS3, for short.
2 requires 3 operations as 2 = floor(sqrt(3!)) or FS(3!), for short.

Title: Re: Square Root, Floor, and Factorial
Post by SMQ on Jan 5^th, 2007, 10:43am

Is the "standard" factorial of a non-integer well defined for this problem? If not, I'm seeing:

4. [hide]FSSSSSS((FSSSSSSS(((FSS(3!!))!!))!)[/hide] (23 operations)
5. [hide]FSS(3!!)[/hide] (5 operations)
6. 3! (1 operation)
7. [hide]FSSSSSSSSSSS(3!!!)[/hide] (15 operations)
8. [hide]FSS((FSSSSSSSSSSS(3!!!))!)[/hide] (19 operations)
9. [hide]FSSSS((FSSSSSSSSS((FSSSS((FSSSSSSS((FSS(3!!))!!))!))!))!)[/hide] (38 operations)

[edit] expanded references and added 9 from below [/edit]

--SMQ

Title: Re: Square Root, Floor, and Factorial
Post by THUDandBLUNDER on Jan 5^th, 2007, 11:21am

on 01/05/07 at 10:43:45, SMQ wrote:

Is the "standard" factorial of a non-integer well defined for this problem?
--SMQ

Nope.

Title: Re: Square Root, Floor, and Factorial
Post by SMQ on Jan 5^th, 2007, 12:10pm

9. [hide]FSSSS((FSSSSSSSSS((FSSSS((FSSSSSSS((FSS(3!!))!!))!))!))!)[/hide] (38 operations)

--SMQ

Title: Re: Square Root, Floor, and Factorial
Post by ThudanBlunder on Apr 30^th, 2007, 12:00pm

on 01/05/07 at 12:10:18, SMQ wrote:

9. [hide]FSSSS((FSSSSSSSSS((FSSSS((FSSSSSSS((FSS(3!!))!!))!))!))!)[/hide] (38 operations)
--SMQ

Can be done in 36