?5?7?7?4? = 34

[Yerushalmi]

So we just had the Jewish New Year 5774, and one of my local newsletters has challenged its readers to use the digits in the new year in various combinations to get every integer from 1 onward. For instance:

5*7/7-4 = 1
5+7/7-4 = 2
5*7/7-√4 = 3
(-5+7)*((7-4)!)= 12
√((5+7+7))^(√4)) = 19
√((5*√(7*7))^√4) = 35
5!-7*7-4! = 47
et cetera.

I've so far managed to get every number from 1 to 55 and climbing. But I can't get 34 (and there's no guarantee it's possible).

Anyone want to help me get 34? :)

[Formalhaut]

:whoa:

[The Man]

Can you only use each number once? If not then it should be easy. If you can only use each number once, then yeah, it might be impossible.

[Yerushalmi]

Not only can you use them once each (because otherwise it's idiotic :tongue:), but they need to be used in order as well. Otherwise I could've just done 5*4+7+7.

34 is trivial to obtain if you can figure out how to do any of the following:
-Eliminate the 5, the way I eliminated the 4 in obtaining 19, and eliminated a 7 and the 4 in obtaining 35 (see the original post)
-Turn the two 7s into a 2 or 5
-Turn the 5 and first 7 into a 3 or a 6
-Turn the second 7 and the 4 into a 0 or 1

[The Man]

smurf. Yeah, it's much too early in the morning for me to be able to figure any of that out.

I did think it would be rather silly if you could use each number more than once, but having to use each number in order makes it tricky.

[Tigmafuzz]

use the digits in the new year in various combinations

Judging from your examples, I'm assuming the digits have to stay in order. An easy solution would be 5*7-((7+4)^0) but that's assuming you can add a zero at the end as an exponent. If that's not an option, then the just as easy solutions would be either:

⌈5√7 + 7 * 4⌉ which is a ceiling function of the 5th root of 7 (≈1.476) plus 7 (which gives us 8.476) multiplied by 4 (which gives us 33.9, and the ceiling function automatically rounds that up to the nearest integer, which is 34.)

or, if you're putting it in a calculator:

⌈5 yroot 7 + 7 * 4⌉ which gives the same result, because the ceiling function is cool like that.
EDIT: if you're putting the previous function in the calculator, you would actually press 7 yroot 5. This function is a different equation entirely that just so happens to also end up with a number between 33 and 34.

Another weird solution, using the floor function instead, would be:

⌊5! / 7 - 7⌋ + 4! which is a floor function of the factorial of 5 (120) divided by 7 (which gives us ≈17.143) minus 7 (leaving us with ≈10.143, which the floor function rounds down to 10) plus the factorial of 4 (which is 24, giving us a total of 34.)

Math is fun.

EDIT2: 5+7+7+4x where x=3.75
lol cheating

[Yerushalmi]

Haha! No, I can't add 0s. If I could, then I'd simply do 5+7+7+4+0!+0!+0!+0!+0!.... etc.

I like your other solutions! I hadn't known floor and ceiling functions had symbols. I'm a little afraid to use them - I think I'm pushing it just having used factorials - but I'll list it for now, and replace it if I can find anything 'simpler'.

In the meantime, I'm only missing two of the numbers between 55-69.

[Tigmafuzz]

What are they? Lemme at 'em.

[Yerushalmi]

Nah, I want to give myself a fair crack at them first. I only posted 34 up here because it's been almost a week and I'm desperate :p

EDIT: Grumble. I thought I had it. I need to turn the last 7 and 4 into a 1 or 0 so I can subtract 1 or 0! from 5*7. I've managed to eliminate the final 7 and 4 by doing 7!/(7-4)! = 7, but that doesn't turn them into a 0, it just erases them. Damn!

[Old Manus]

It's times like these that confirm to me that I was never cut out for grad school anyway.

[Tigmafuzz]

>mfw Americans call onesies-twosies-redsies-bluesies "Mathematics"

[Endless]

If I'm allowed letters :
47438

Edit : another way, modulus ftw.
5*7 - (7! mod 4!)! = 34

[Yerushalmi]

If I'm allowed letters :
47438

Edit : another way, modulus ftw.
5*7 - (7! mod 4!)! = 34

Oooh! Except instead of letters, using % for modulus would work:
5*7-(7!%4!)!

Awesome!

[Shorty]

I have nothing of value to contribute to this thread, but it is making my head spin.

[Pheesh]

http://stream1.gifsoup.com/view5/2047169/homer-thinking-o.gif

[Tigmafuzz]

I completely forgot 0!=1 xD

[Yerushalmi]

Thanks to Endless's contribution I am only missing six of the numbers from 1 to 100 :)

Using the percent symbol for modulus is recognized by google's calculator feature, so I can justify using it. In added modulus to my toolbox of functions, I was able to figure out three or four really difficult ones that had evaded me thus far.

[Parker]

I've never seen modulus not represented by a %. What else is used?

I have this weird thing where I find maths interesting and fascinating but I am absolutely terrible at it. Adding two numbers makes me cringe. The maths part of my mind is utterly dyslexic.

[Yerushalmi]

"mod". Which is also recognized by Google's calculator feature, but I'm not so comfortable using letters.

It's not so weird that enjoying something, or appreciating something, is completely divorced from ability. I am absolutely enthralled with the costuming and makeup artistry abilities of others, but I'd be absolutely terrible at it myself.

EDIT: I am now only missing 92, 94, and 100.

EDIT: Found 92.

[Endless]

94 is actually simple:
5*(7+7)+4! = 94

100 requires using the digits in a different way, but they're all there, in the right order:
(57-7)*√4 = 100

Edit : actually, you don't even need that.
(-5+7!!)%((7+4)!)=100 (http://www.wolframalpha.com/input/?i=%28-5%2B7!!%29%25%28%287%2B4%29!%29)

[Yerushalmi]

94 is actually simple:
5*(7+7)+4! = 94

100 requires using the digits in a different way, but they're all there, in the right order:
(57-7)*√4 = 100

Oh wow, well done. I probably would've gotten the former eventually, not necessarily the latter (though I've used 57, 77, and 74 multiple times). I blame it on lack of sleep thanks to my daughter waking me up at 5:30am demanding that I help her dress up her Belle doll.

When I'm not half-dead with exhaustion I'll post the entire 1-100 list.

[noxious.sunshine]

Get outta here with that craziness!

1+1= 11. Or a Window. Depending on how you look at it.

[Yerushalmi]

The numbers 1-100, in order:

5*7/7-4
5+7/7-4
5*7/7-√4
5*(7-7)+4
5+(7-7)*4
(-5+7)*(7-4)
5*7-7*4
5-7/7+4
5*7/7+4
5+7/7+4
-5+7+7+√4
(-5+7)*((7-4)!)
-5+7+7+4
5+√(7*7)+√4
5+7+7-4
5+√(7*7)+4
5+7+7-√4
(-5+7)(7+√4)
√((5+7+7))^(√4))
5*(7/7)*4
5+7+7+√4
(-5+7)(7+4)
5+7+7+4
5*(7-7)+4!
5*(7/7+4)
5*7-(7+√4)
(5+7*7)/√4
√((5*7-7)^√4)
5*7-(7-4)!
-5+7+7*4
5*√(7*7)-4
5*7-7+4
5*√(7*7)-√4
5*7-((7!)%(4!))!
√((5*√(7*7))^√4)
5+√(7*7)+4!
5*√(7*7)+√4
5*7+7-4
5*√(7*7)+4
-5+7*7-4
5*7+(7-4)!
-5+7*7-√4
5+7+7+4!
5*7+7+√4
5!-77+√4
57-7-4
5!-7*7-4!
5!*.7/7*4
5*7+7*√4
5+7*7-4
-5+(7+7)*4
5*7-7+4!
5!+7-74
(5*7/.7)+4
5*(√(7*7)+4)
(-5+7)*7*4
57+(7!)%(4!)
5+77-4!
5*√(7*7) +4!
57+7-4
5+7+7^√4
-5-7+74
57+(7-4)!
√((57+7)^√4)
5*(7+(7-4)!)
57+7+√4
5!-7*7-4
57+7+4
5!-7*7-√4
-5+77-√4
57+7*√4
√((-5+77)^√4)
5!-7*7+√4
-5+77+√4
5!-7*7+4
-5+77+4
√((5!*.7-7)^√4)
5+77-4
5%7+74
5+77-√4
(-5+7+7)^√4
5!-7-7-4!
-5!-7+7!/4!
5+77+√4
57+7*4
5+77+4
5!*.7+7-4
57+7+4!
-5+7*7*√4
5*(7+7+4)
√((5!*.7+7)^√4)
5!-√(7*7)*4
-5+7*7*√4
5*(7+7)+4!
5!-7*7+4!
5!+7-7-4!
-5!+7+7!/4!
(-5+7)*(7^√4)
5!-7-7*√4
(57-7)*√4

[Jiro]

I've never seen modulus not represented by a %. What else is used?

I have this weird thing where I find maths interesting and fascinating but I am absolutely terrible at it. Adding two numbers makes me cringe. The maths part of my mind is utterly dyslexic.

Yeah I love but suck completely at mathematics.

[Quindiana Jones]

NEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRDSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS.

[Pike]

Yeah I love but suck completely at mathematics.

For me it depends on the teacher, with a good teacher I rock the socks off of math. With a poor one I'm not so hot. I do find mathematics to be absurdly beautiful; I think numerical patterns and proofs are more gorgeous than any art form.

I'm much, much too out of practice to be of any help in this thread, however. Been out of school for too long.

[Yerushalmi]

I'm much, much too out of practice to be of any help in this thread, however. Been out of school for too long.

I haven't taken a math class in ten years. But I'm not out of practice, because I play plenty of math games like this one in my spare time. The latter quoted sentence is an excuse, not a reason, for the former :p