Five Fives Game

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Re: Five Fives Game

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

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Re: Five Fives Game

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.

maasman

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Re: Five Fives Game

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)!

crispybits

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Re: Five Fives Game

317 = Γ5 x 5!! + 5 - Γ5 - Γ5
317 = 24 x 15 + 5 - 24 - 24
317 = 360 - 43
317 = 317

maasman

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Re: Five Fives Game

331 = Γ5 x 5!! - 5# + 5/5
331 = 24 x 15 - 30 + 1
331 = 360 - 29
331 = 331

crispybits

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Re: Five Fives Game

337 = Γ5 x 5!! + 5/5 - Γ5
337 = 24 x 15 + 1 - 24
337 = 360 - 23
337 = 337

maasman

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Re: Five Fives Game

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

crispybits

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Re: Five Fives Game

349 = Γ5 x 5!! + Γ5 - 5# - 5
349 = 24 x 15 + 24 - 35
349 = 360 - 11
349 = 349

maasman

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Re: Five Fives Game

353 = (Γ5 x 5!!) - (.5 x 5!!) + .5
353 = (24 x 15) - (.5 x 15) + .5
353 = 360 - 7.5 + 0.5
353 = 353

crispybits

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Re: Five Fives Game

359 = Γ5 x 5!! - (√5 x √5)/5
359 = 24 x 15 - 5/5
359 = 360 - 1
359 = 359

maasman

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Re: Five Fives Game

367 = (Γ5 x 5!!) + (.5 x 5!!) - .5
367 = (24 x 15) + (.5 x 15) - .5
367 = 360 + 7.5 - 0.5
367 = 367

crispybits

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Re: Five Fives Game

365=5!+5!+5*5*5 (nobody did this number!!!)
This image is a sofilorry.

Eddygp

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Re: Five Fives Game

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

crispybits

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Re: Five Fives Game

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

crispybits

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Re: Five Fives Game

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?)

crispybits

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Re: Five Fives Game

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.

maasman

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Re: Five Fives Game

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

crispybits

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Re: Five Fives Game

So what's the new rule? we can use any function except floor/ceiling?
From: Karl_R_Kroenen

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Re: Five Fives Game

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.

crispybits

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Re: Five Fives Game

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.

maasman

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Re: Five Fives Game

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 )

crispybits

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Re: Five Fives Game

Because I'm lazy:

389 = (5+5!!/5)!! + √5 x √5
389 = (5+3)!! + 5
389 = 384 + 5
389 = 389

maasman

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Re: Five Fives Game

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

crispybits

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Re: Five Fives Game

401 = 5# x 5!! - 5 x 5 - Γ5
401 = 30 x 15 - 25 - 24
401 = 450 - 49
401 = 401

maasman

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Re: Five Fives Game

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

crispybits

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