Five Fives Game

[maxfaraday]

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

[maasman]

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.

[crispybits]

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)!

[maasman]

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

[crispybits]

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

[maasman]

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

[crispybits]

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

[maasman]

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

[crispybits]

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

[maasman]

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

[crispybits]

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

[Eddygp]

365=5!+5!+5*5*5 (nobody did this number!!!)

[crispybits]

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]

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]

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?)

[maasman]

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.

[crispybits]

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

[maxfaraday]

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

[crispybits]

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.

[maasman]

379 = (5+5!!/5)!! - √5 x √5
379 = (5+3)!! - 5
379 = 384 - 5
379 = 379

[crispybits]

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 )

[maasman]

Because I'm lazy:

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

[crispybits]

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

[maasman]

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

[crispybits]

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