# The Four Fours Problem

James Chegwidden

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posted 13 years ago

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.

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.

Author and Instructor, my book

Melvin Menezes

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Greg Harris

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posted 13 years ago

this is assuming i can use mod(x,y) and !

1 = (4/4)*(4/4)

2 = (4*4)/(4+4)

3 = ((4*4)-4)/4

4 = (4*(4-4))+4

5 = MOD((4/4),4)+4

6 = (SQRT(4))+(4-4)+4

7 = ((4+SQRT(4))+(4/4))

8 = ((4+4)*4)/4

9 = (4+4)+(4/4)

10 = (4!+SQRT(4)-4*4)

11 = (4!/SQRT(4))-(4/4)

12 = (4!+4-4*4)

13 = (4!/SQRT(4))+(4/4)

14 = (4*4)-(4/SQRT(4))

15 = (4*4)-(4/4)

16 = (4/4)*(4*4)

17 = (4*4)+(4/4)

18 = ((4*4)+4)-(SQRT(4))

19 = (4!-4-4/4)

20 = (4*(4/4+4))

1 = (4/4)*(4/4)

2 = (4*4)/(4+4)

3 = ((4*4)-4)/4

4 = (4*(4-4))+4

5 = MOD((4/4),4)+4

6 = (SQRT(4))+(4-4)+4

7 = ((4+SQRT(4))+(4/4))

8 = ((4+4)*4)/4

9 = (4+4)+(4/4)

10 = (4!+SQRT(4)-4*4)

11 = (4!/SQRT(4))-(4/4)

12 = (4!+4-4*4)

13 = (4!/SQRT(4))+(4/4)

14 = (4*4)-(4/SQRT(4))

15 = (4*4)-(4/4)

16 = (4/4)*(4*4)

17 = (4*4)+(4/4)

18 = ((4*4)+4)-(SQRT(4))

19 = (4!-4-4/4)

20 = (4*(4/4+4))

what?

Melvin Menezes

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Greg Harris

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posted 13 years ago

sorry... i should have posted a link to my attempt, rather than the solutions.

i wish i had thought of

(oops, i used html code)

[ June 03, 2003: Message edited by: Greg Harris ]

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 ]

what?

Mark Herschberg

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Greg Harris

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posted 13 years ago

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.

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.

what?

John Lee

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posted 13 years ago

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 ]

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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John Lee

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