[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 236

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It comes out the same as in the original. But it's clearer (?).

It's all about the algorithm. Then mathematical formulas as a bonus )

 

Well, yes, excellent. You've solved the main part of the puzzle. Now all that's left is the small part. C-4, you'll figure it out on your own?

P.S. I'm seriously interested in 1+...+m = n! Obvious solutions are at n = 1, 3, 5. I got to n = 29 - no solutions yet.

 
Mathemat писал(а) >>

I've bruteforced it to n = 30 - no solutions yet.

Well, that's overkill. And I was asked to do it verbally. It's faster if you do it by computer :)

 

You can't go through all the solutions with a computeraire anyway (you need proof).

 

Ooh, the hell with it!

[1-50]!

1
2
6
24
120
720
5040
40320
362880
3628800
39916800
479001600
6227020800
87178291200
1307674368000
20922789888000
355687428096000
6402373705728000
121645100408832000
2432902008176640000
51090942171709400000
1124000727777610000000
25852016738885000000000
620448401733239000000000
15511210043331000000000000
403291461126606000000000000
10888869450418400000000000000
304888344611714000000000000000
8841761993739700000000000000000
265252859812191000000000000000000
8222838654177920000000000000000000
263130836933694000000000000000000000
8683317618811890000000000000000000000
295232799039604000000000000000000000000
10333147966386100000000000000000000000000
371993326789901000000000000000000000000000
13763753091226300000000000000000000000000000
523022617466601000000000000000000000000000000
20397882081197400000000000000000000000000000000
815915283247898000000000000000000000000000000000
33452526613163800000000000000000000000000000000000
1405006117752880000000000000000000000000000000000000
60415263063373800000000000000000000000000000000000000
2658271574788450000000000000000000000000000000000000000
119622220865480000000000000000000000000000000000000000000
5502622159812090000000000000000000000000000000000000000000
258623241511168000000000000000000000000000000000000000000000
12413915592536100000000000000000000000000000000000000000000000
608281864034268000000000000000000000000000000000000000000000000
30414093201713400000000000000000000000000000000000000000000000000
 

How many significant characters can an integer have?

Ah, I see, these are imprecise values...

 
i.e. it rounds up ( ?
 

Well yes, it looks like 15 significant digits at the most.

P.S. 50! zeros on the right-hand side should have 12 exactly, but there's a whole bunch of them.

 

Here, I drew it in excel. And it turns out that for

for every Y there's a pair of X's.)

Oh, yeah, they have to be integers...


 

Of course, the trick is all in their integers.

1...229230231232233234235236237238239240241242243...628
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