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        riddles >> easy >> Expressing the number 77 using 1,2,3,4
        
(Message started by: Bill Cheong on Nov 9^th, 2004, 3:02pm)

Title: Expressing the number 77 using 1,2,3,4
Post by Bill Cheong on Nov 9^th, 2004, 3:02pm

Express the number using the digits 1,2,3 and 4 by means of a formula that uses each digit exactly once. Any combination of elementary operations (including factorials) and decimal numbers are allowed.

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Sir Col on Nov 9^th, 2004, 3:40pm

Can I do [hide]4*2/.1-3[/hide]?

Title: Re: Expressing the number 77 using 1,2,3,4
Post by bob on Nov 9^th, 2004, 10:28pm

??? (3+4)(2x4+3)

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Barukh on Nov 10^th, 2004, 12:00am

bob, it seems you are using the digit '4' twice.

Couple of other examples:

[smiley=square.gif][hide]
(31 - .2)/.4
3!^2 + 41
[/hide][smiley=square.gif]

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Barukh on Nov 10^th, 2004, 1:54am

How about expressing 94, 95, 97 using the same digits? This time, factorial is not allowed!

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Fresno_Bob on Nov 10^th, 2004, 6:51am

Well, pretty close...

4^(3.1+.2) ~ 97.00586

Can I clip it with the floor function? Then
[hide]
94 = floor(3.1^4+2)
95 = ceil(3.1^4+2)
97 = floor(4^(3.1+.2))
[/hide]

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Sir Col on Nov 10^th, 2004, 4:38pm

If the rounding functions are not allowed, I've found 94 and 97 using more elementary operations and 95 by a more questionable approach...

::[hide]
94=3²/.1+4
95=2*atan(1)+sqrt(4)+3
97=(sqrt(4)/.2-.3)/.1

And if atan is allowed, then we could use asin(1) as a building block for 90, which seems a little cheeky.
[/hide]::

Title: Re: Expressing the number 77 using 1,2,3,4
Post by TenaliRaman on Nov 10^th, 2004, 8:14pm

::[hide]90 = 12*3/.4[/hide]::

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Barukh on Nov 10^th, 2004, 11:19pm

on 11/10/04 at 06:51:39, Fresno_Bob wrote:

Can I clip it with the floor function?

No.

on 11/10/04 at 16:38:58, Sir Col wrote:

And if atan is allowed

It is not allowed.

Also, [hide]can you make 97 without using square root[/hide]? ;)

Title: Re: Expressing the number 77 using 1,2,3,4
Post by Barukh on Nov 19^th, 2004, 1:50am

Is this thread out of interest? Anyway, here's an answer to my last question to Sir Col:

[smiley=blacksquare.gif][hide]97 = .1 ^ (2-4) - 3[/hide][smiley=blacksquare.gif]