Five Fives Game

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Re: Five Fives Game

Postby maxfaraday on Sun Apr 07, 2013 7:14 am

actually can we know exactly what all the symbols mean?
"!!" seems to be the sum, but i'm not sure about the others...
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Re: Five Fives Game

Postby maasman on Sun Apr 07, 2013 8:02 am

maxfaraday wrote:actually can we know exactly what all the symbols mean?
"!!" seems to be the sum, but i'm not sure about the others...


!! is the double factorial only multiplying every other number in the sequence, so 5!! = 1 x 3 x 5 = 15, or 6!! = 2 x 4 x 6 = 48 and so on.
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Re: Five Fives Game

Postby crispybits on Sun Apr 07, 2013 8:03 am

313 = (5^5 + 5) / (5 + 5)
313 = (3125 + 5) / 10
313 = 3130 / 10
313 = 313

Also Γ5 (or gamma 5) is the factorial of the number one less

So Γn = (n-1)!
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Re: Five Fives Game

Postby maasman on Sun Apr 07, 2013 9:08 am

317 = Γ5 x 5!! + 5 - Γ5 - Γ5
317 = 24 x 15 + 5 - 24 - 24
317 = 360 - 43
317 = 317
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Re: Five Fives Game

Postby crispybits on Sun Apr 07, 2013 11:36 am

331 = Γ5 x 5!! - 5# + 5/5
331 = 24 x 15 - 30 + 1
331 = 360 - 29
331 = 331
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Re: Five Fives Game

Postby maasman on Sun Apr 07, 2013 4:07 pm

337 = Γ5 x 5!! + 5/5 - Γ5
337 = 24 x 15 + 1 - 24
337 = 360 - 23
337 = 337
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Re: Five Fives Game

Postby crispybits on Sun Apr 07, 2013 4:19 pm

347 = Γ5 x (5!! - .5) - 5/5
347 = 24 x (15 - .5) - 1
347 = 24 x 14.5 - 1
347 = 348 - 1
347 = 347

Only way I could do it without floor/ceiling
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Re: Five Fives Game

Postby maasman on Sun Apr 07, 2013 4:33 pm

349 = Γ5 x 5!! + Γ5 - 5# - 5
349 = 24 x 15 + 24 - 35
349 = 360 - 11
349 = 349
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Re: Five Fives Game

Postby crispybits on Sun Apr 07, 2013 4:35 pm

353 = (Γ5 x 5!!) - (.5 x 5!!) + .5
353 = (24 x 15) - (.5 x 15) + .5
353 = 360 - 7.5 + 0.5
353 = 353
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Re: Five Fives Game

Postby maasman on Mon Apr 08, 2013 2:44 am

359 = Γ5 x 5!! - (√5 x √5)/5
359 = 24 x 15 - 5/5
359 = 360 - 1
359 = 359
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Re: Five Fives Game

Postby crispybits on Mon Apr 08, 2013 3:57 am

367 = (Γ5 x 5!!) + (.5 x 5!!) - .5
367 = (24 x 15) + (.5 x 15) - .5
367 = 360 + 7.5 - 0.5
367 = 367
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Re: Five Fives Game

Postby Eddygp on Mon Apr 08, 2013 9:55 am

365=5!+5!+5*5*5 (nobody did this number!!!)
Nothing will come of nothing.
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Re: Five Fives Game

Postby crispybits on Mon Apr 08, 2013 10:20 am

Hehe - we're just doing primes up until 1001 I think now eddygp - it's all a bit too easy to get to any 3 figure number so as long as we can make all the primes we'll assume the rest are pretty simple.

Next one is 373
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Re: Five Fives Game

Postby crispybits on Tue Apr 09, 2013 3:04 am

OK I can do 373 with floor and ceiling (obscenely easy), but to do it without.... that's a tough one. Took me ages to figure it out.

373 = (5!! + .5) x Γ5 + 5/5
373 = 15.5 x 24 + 1
373 = 372 + 1
373 = 373

Next target = 379
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Re: Five Fives Game

Postby crispybits on Tue Apr 09, 2013 5:11 am

For those who have been asking about the meanings of different symbols and functions, I've just been backwards and forwards through wikipedia's maths section and found every function that I think could be useful. I'll hide them in a spoiler in case people don't want to see them, but this isn't a template to just read off the answers, just a description of how all the different functions work. I've left out a few that aren't really useful.

We've used most of them, but there's a few here we haven't touched yet that may come in handy as we get higher targets.

show


I'd suggest we limit nesting to 2 levels, otherwise we could end up with f(f(f(f(f(x))))) which is no fun, so you can do φ(Π(5!!)) but no more than that? (that one works out at 8 by the way)

(Or am I just horribly overcomplicating this and we stick to a smaller list of allowed functions?)
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Re: Five Fives Game

Postby maasman on Tue Apr 09, 2013 6:29 am

I'm fine with more functions. The main reason why I dislike the ceiling/floor functions is that you can abuse them to essentially get any number you want out of a single 5 by just using repeated square rooting and random other functions.

Also, I can't figure out 373 without using the ceiling/floor functions.
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Re: Five Fives Game

Postby crispybits on Tue Apr 09, 2013 6:32 am

I got 373 without ceiling/floor already:

373 = (5!! + .5) x Γ5 + 5/5
373 = 15.5 x 24 + 1
373 = 372 + 1
373 = 373

Next target = 379
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Re: Five Fives Game

Postby maxfaraday on Tue Apr 09, 2013 10:06 pm

So what's the new rule? we can use any function except floor/ceiling?
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Re: Five Fives Game

Postby crispybits on Wed Apr 10, 2013 1:50 am

I think we've always been able to use any function, just now I've made a list of them that's as complete as I can find infor for - we still can use floor/ceiling but maasman and I are avoiding them if possible.
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Re: Five Fives Game

Postby maasman on Wed Apr 10, 2013 11:49 am

379 = (5+5!!/5)!! - √5 x √5
379 = (5+3)!! - 5
379 = 384 - 5
379 = 379
Last edited by maasman on Wed Apr 10, 2013 12:18 pm, edited 1 time in total.
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Re: Five Fives Game

Postby crispybits on Wed Apr 10, 2013 12:12 pm

383 = σ(5!) + 5! + 5!! + 5 + Π5
383 = 240 + 120 + 15 + 5 + 3
383 = 383

(having done all that bloomin research I've gotta slip some of the "new" ones in there :-P)
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Re: Five Fives Game

Postby maasman on Wed Apr 10, 2013 12:18 pm

Because I'm lazy:

389 = (5+5!!/5)!! + √5 x √5
389 = (5+3)!! + 5
389 = 384 + 5
389 = 389
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Re: Five Fives Game

Postby crispybits on Wed Apr 10, 2013 12:37 pm

397 = Γ5 x (5!! + (Π5 x .5)) + μ(5!!)
397 = 24 x (15 + (3 x .5)) + 1
397 = 24 x 16.5 + 1
397 = 396 + 1
397 = 397
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Re: Five Fives Game

Postby maasman on Wed Apr 10, 2013 1:13 pm

401 = 5# x 5!! - 5 x 5 - Γ5
401 = 30 x 15 - 25 - 24
401 = 450 - 49
401 = 401
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Re: Five Fives Game

Postby crispybits on Wed Apr 10, 2013 1:55 pm

409 = Γ5 x (5!! + σ(5!!)) + 5/5
409 = 24 x (15 + 2) + 1
409 = 24 x 17 + 1
409 = 408 + 1
409 = 409
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