Here is a problem that I found in a rec math book from the 1950's This is an old problem consisting of expressing successive integers (to a limit) in appropriate mathematical form, using only 4 (four) fours (4's) in each expression together with any necessary signs. Note: My math collegues had a field day with this problem. Examples: 1 = 4/4 * 4/4 10 = (44 -4)/4 So for what are the first twenty numbers written in only 4 4's.

17 == (4*4)+(4/4) Ah! Greg hit post button before i did! Using a . was smart, David. [ June 03, 2003: Message edited by: Melvin Menezes ]

Greg Harris
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sorry... i should have posted a link to my attempt, rather than the solutions. i wish i had thought of 44 and 0.4... things would have been much easier! (oops, i used html code) [ June 03, 2003: Message edited by: Greg Harris ]

I did a variation of this in 6th grade. You can do all the numbers 0 to 100. --Mark

Greg Harris
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actually, after googling around, this guy says you can go from 0 to 40,000. here is a short list that goes from 0 to 1,000. not quite the same as what i came up with... and i did not think about using sin, cos, gamma, etc.

there is an old game: pick any 4 playing cards, use only "+", "-", "x", "/" to get 24. the introduction of "mod", "sqrt", and so on makes it simpler. so why i can not use self defined functions? [ June 04, 2003: Message edited by: Don Liu ]

Greg Harris
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> so why i can not use self defined functions? well, if you provide a proof with your function, then you can use it!

John Lee
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let CVFD(4444) = 21, so, 21 = CVFD(4444) for any number X, i can define a function XXX(), let XXX(4444) = X