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wu :: forums    riddles    putnam exam (pure math) (Moderators: Grimbal, SMQ, Icarus, towr, william wu, Eigenray)    Square Root, Floor, and Factorial « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Square Root, Floor, and Factorial  (Read 1616 times) ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Square Root, Floor, and Factorial   « on: Jan 5th, 2007, 10:00am » Quote Modify 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. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Square Root, Floor, and Factorial   « Reply #1 on: Jan 5th, 2007, 10:43am » Quote Modify Is the "standard" factorial of a non-integer well defined for this problem?  If not, I'm seeing:   4. FSSSSSS((FSSSSSSS(((FSS(3!!))!!))!) (23 operations) 5. FSS(3!!) (5 operations) 6. 3! (1 operation) 7. FSSSSSSSSSSS(3!!!) (15 operations) 8. FSS((FSSSSSSSSSSS(3!!!))!) (19 operations) 9. FSSSS((FSSSSSSSSS((FSSSS((FSSSSSSS((FSS(3!!))!!))!))!))!) (38 operations)   [edit] expanded references and added 9 from below [/edit]   --SMQ « Last Edit: Jan 5th, 2007, 12:13pm by SMQ » IP Logged --SMQ ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Square Root, Floor, and Factorial   « Reply #2 on: Jan 5th, 2007, 11:21am » Quote Modify on Jan 5th, 2007, 10:43am, SMQ wrote: Is the "standard" factorial of a non-integer well defined for this problem? --SMQ Nope. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. SMQ wu::riddles Moderator Uberpuzzler     Gender: Posts: 2084 Re: Square Root, Floor, and Factorial   « Reply #3 on: Jan 5th, 2007, 12:10pm » Quote Modify 9. FSSSS((FSSSSSSSSS((FSSSS((FSSSSSSS((FSS(3!!))!!))!))!))!) (38 operations)   --SMQ IP Logged --SMQ ThudnBlunder Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Square Root, Floor, and Factorial   « Reply #4 on: Apr 30th, 2007, 12:00pm » Quote Modify on Jan 5th, 2007, 12:10pm, SMQ wrote: 9. FSSSS((FSSSSSSSSS((FSSSS((FSSSSSSS((FSS(3!!))!!))!))!))!) (38 operations) --SMQ Can be done in 36 IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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