Questions 3: The number 916238457 is an example of a nine-digit number which contains each of the digits 1 to 9 exactly once. It also has the property that the digits 1 to 5 occur in their natural order, while the digits 1 to 6 do now. How many such numbers are there?
I would like the numerical answer to this, but please only answer if you did the BMO 2006 and have a proof as well.
2006-12-01 07:45:59 · 2 answers · asked by Mark R 2 in Science & Mathematics ➔ Mathematics
I have already DONE the paper! (and kinda failed). I'm asking because I got a numerical answer to that question, but without a proof or time to write a proof, and I want to know whether the answer I have is correct. So no, I'm not cheating, I just want to know whether my answer is correct.
2006-12-01 08:13:24 · update #1
Quit yer cheatin,and do the dad-burn easy thing yerself....
2006-12-01 07:49:14 · answer #1 · answered by Anonymous · 0⤊ 2⤋
Well, I didn't do the BMO, but I've done some IMOs so I may be able to help ;)
edit - oops, sorry. I realised you only wanted the number not the proof.
The number is 2520.
Don't read any further if you don't want, but I'm going to leave the proof here, ROT13-ed so that you don't accidentally read it without wanting to (go to rot13.com to decode it).
Svefgyl, yrgf vtaber gur erfgevpgvba nobhg abg univat 1-6 va n ebj. Ubj znal ahzoref unir 1-5 va n ebj?
Gurer ner 9 cbfvgvbaf va gur ahzore. Jr arrq gb pubbfr 5 bs gurz - bapr jr unir pubfra 5, jr jevgr 1,2,3,4,5 va gubfr 5 cbfvgvbaf. Guhf, gurer ner 9P5 = 126 jnlf gb pubbfr gubfr 5 cbfvgvbaf. Nsgre qbvat gung, jr pna jevgr va gur 6,7,8,9 va 4! jnlf. Guhf jr unir 9P5 * 4! = 3024.
Abj, fbzr bs gubfr pbagnva 1 gb 6 va n ebj. Ubj qb jr ryvzvangr gubfr? Whfg pbhag ubj znal unir 1 gb 6 va n ebj, naq fhogenpg sebz gur nobir.
Jr qb gung va rknpgyl gur fnzr jnl: 9P6 jnlf gb pubbfr gur 6 cbfvgvbaf, 3! jnlf gb neenatr 7,8,9, tvivat 504.
Guhf gur nafjre vf 3024 - 504 = 2520.
2006-12-01 16:46:39 · answer #2 · answered by stephen m 4 · 1⤊ 1⤋