4 Numbers, to equal others

[da_silvy]

OK

i have a bit of a maths problem

I want to find, from 1 to 100 how four 4's can be used to make that number

e.g

1 = (4+4) / (4+4) or (4/4) / (4/4)
2 = (4/4) + (4/4)

and so on

I have worked out all, but the following:

35,
37,
39,
41,
43,
45,
51,
53,
55,
57,
71,
73,
75,
77,
83,
85,
87,
89,
91,
93,
99,

If anyone can help with the solution to any of these, please post

BTW:

Factorial, e.g. 4! = (24) can be used, so can Root(4) = (2), squares, cubes and powers can be used

e.g.

4^2, 4^3, 4^4, 4^x

etc

please help with the above numbers

[da_silvy]

ahh come on?

no one knows?

[da_silvy]

ahh come on, where are all you gurus?

[Starman]

35=(4+(4/4)+(4/4))*(4+(4/4)+(4/4)) - (4/4)

or ((4!)/4)*((4!)/4) - (4/4)


does this count?

If it does then the others should be easy - just a bit long

[da_silvy]

no,

only 4 numbers can be used

e.g.

26 can be

4! + 4 - 4 + Sqr(4)

which is basically 24 + 2 = 26

[Starman]

ah right, sorry I missed that.

[da_silvy]

ohhh

i thought you had some solutions for me

[HarryW]

35 is (4^3 + 4 + sqr(4)) / sqr(4)

[DavidHooper]

i remember reading it is possible for all but two numbers in the range 1-99.

can't u just write a program to do it?

[NotLKH]

Originally posted by da_silvy
OK


I have worked out all, but the following:

35,
37,
39,
41,
43,
45,
51,
53,
55,
57,
71,
73,
75,
77,
83,
85,
87,
89,
91,
93,
99,

If anyone can help with the solution to any of these, please post

BTW:
.....and powers can be used

e.g.

4^2, 4^3, 4^4, 4^x

etc

Heres a jumping off point for some:

85 = 4^3 + 4^2 + 4^1 + 4^0
83 = 4^3 + 4^2 + 4^1 - 4^0
77 = 4^3 + 4^2 - 4^1 + 4^0
75 = 4^3 + 4^2 - 4^1 - 4^0

etc...
-Lou

[riis]

Is this also allowed?

99 = 4^3.5 - 4^2.5 + 4 - 4^0

You didn't say powers should be integers (besides, sqrt is also used, which is a power of 0.5)

[NotLKH]

Looks like its legal to use non-integer values.
Or, for that matter, (a + sqr(b)), (a - sqr(b)) values. with the proper combination, ALL integer numbers could be generated this way.

{ Although, I personally think only 4's should be used for any number. IMHO }

[kedaman]

hmm, whats the first number that can't be described this way
99=4!*4+4-4^0
93=4!*4-4+4^0
91=4!*4-4-4^0
89=4^3+4!+4^0*4^0
87=4^3+4!-4^0*4^0
73=4^3+4*sqr(4)+4^0
71=4^3+4*sqr(4)-4^0
57=4^3-4-4+4^0
55=4^3-4-4-4^0
53=4^3-4^2+4+4^0
51=4^3-4^2+4-4^0
45=4!+4!-4+4^0
43=4!+4!-4-4^0
41=4!+4^2+4^0*4^0
39=4!+4^2-4^0*4^0
37=24+4^2-sqr(4)-4^0