̤ꤹ
ǤϤ褯륿פǤ
731ڡ 0:09:46 42126
ߤ
ȤƽФΤϡ֣ߡʣݣáˡס
ä⣰ʤΤǡݣäȤƹͤΤϣ
äơߡʣܣܣܡġܣܣˡ᣹ߣᣴ
731ڡ 0:12:02 42127

ɤƤ̤Ȥʤʤ
731ڡ 0:12:25 42128
ǯ
99*(9+8+7+6+5+4+3+2+1)ɤäΤ򡢲򴪰㤤Τ
99*(8+7+6+5+4+3+2+1)99*(7+6+5+4+3+2+1)ܡ99*(2+1)99*1ޤDzäƤޤޤ
ʤΤǷ׻ְ㤤̿õƻ֤ϲ񡣻ǰ
731ڡ 0:17:42 42129
٥륯åĥ
̤񤷤Ǥͤ
ɤǡ˽񤤤ƹͤơ׻ơե೫Ϥ
˰֤DzʬäȤƤ⡢ΥԡɤǤ̵ʵ

ACκ1ΤȤ100-199
2ʤ9923ʤ9939ʤ999
19ޤǤ¤45
99454500-45ʤΤ4455
731ڡ 0:27:01 42130

ϥäȤǤޤߤʤƱȻפޤߤ󤵤ƱǤ羮鷺˰ƣ(ǤǤ͡)ᤵΤ¿ǤΤǤϤʤɤȻפޤ
Ϻꡡ 731ڡ 0:28:22 42131

̲Ƥߤޤ

NΤȤġ5{10^(N/2)-1}^2
NΤȤġ5[10^{(N+1)/2}-1][10^{(N-1)/2}-1]
Ǥ礦ġ

ɵ)ǸȤϡNοդ¤٤ΤȤκΤȤǤ
N=5ʤ顢ABCDE-EDCBAפˤĤƷ׻Ƥޤ
731ڡ 1:31:52 42132
ʪ
ABCCBACAϤ겼Τ10ΰ̤9
100ΰ̤AC1(겼)1ΰ̤10+CAˤʤΤ100ΰ̤1ΰ̤¤AC1+10+CA=9ʤΤǡABC99,198,297,396,495,594,693,792,891ʤΤǡ¤4455
731ڡ 0:42:03 42133

(a+b)*100+a-a*100-a-b=b*100-b
b19ޤǤ
100+200+...+900-(1+2+...+9)=4500-45=4455
Ǥ
731ڡ 0:43:39 42134
Mr.ǥ
#42129κǯԤƱ٤ƤABCΤȤκ¤ȹͤ32,670
ְäפߤ˵դΤ˻֤ꡢƬιŲǧ
ʷɡƱ׻ǡ4455ˡ
731ڡ 1:13:26 42135
⡼ޥ
ä^^;
錄
abc-cba=a(100-1)-c(100-1)=99*(a-c)
a=9...a-c=9~1
a=8a-c=8~1

a=1a-c=1
99*(1*9+2*8+3*7+4*6+5*5+6*4+7*3+8*2+9*1)=16335
ȻפǤޤĤx10äƤ...Orz...
¨ ^^;v 731ڡ 1:36:49 42136
ޤ
ͤ£áݣã£ιפͤơ
ȤƹͤιפäǤ͡
731ڡ 10:10:27 42137
uchinyan
Ϥˤϡơϡ
ϴñǤ͡ʴǡ

ABC CBA κ = |ABC - CBA| = |(A * 100 + B * 10 + C) - (C * 100 + B * 10 + A)|
= |(A - C) * 100 + (C - A)| = |(A - C) * 100 - (A - C) * 1| = |(A - C) * (100 - 1)|
= |(A - C) * 99| = |A - C| * 99
ǡABC 0 9 ʤΤǡ|A - C| 0 9 Ǥ
ǡ¤ϡ
(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) * 99 = 45 * 99 = 4455
ˤʤޤ
ͥνȡ 731ڡ 11:20:25 MAIL:uchi@sco.bekkoame.ne.jp 42138
uchinyan
ǼĤɤߤޤ
ϡʸβ˼㴳θ򤬤ä褦ǤɤΤȤˡƱȻפޤ

ʤ

#42132

NΤȤġ5{10^(N/2)-1}^2
NΤȤġ5[10^{(N+1)/2}-1][10^{(N-1)/2}-1]
Ǥ͡
ͥνȡ 731ڡ 11:43:07 MAIL:uchi@sco.bekkoame.ne.jp 42139
Mr.ǥ
ޤ㤵#42137⡼ޥ󤵤#42136
Ʊߥ򤷤ΤǤABC CBA κ¤ȤȡäΤȤȣäΤȤȤΤ
16335*232670̤ˤȤʤޤ󤫡
731ڡ 12:27:15 42140
ޤ
ͣ򡥥ǥ
᣹ޤƤξͤȣΣܤˤʤޤ󤫡
731ڡ 13:20:12 42141

#42139
uchinyan󡢸ڤꤢ꤬Ȥޤm(__)m

ޡФ餯뤵³Ȥޤɤޤ褦ˡ
731ڡ 13:40:47 42142
Mr.ǥ
ޤ㤵
#42136Υ⡼μڤ
abc-cba=a(100-1)-c(100-1)=99*(a-c)
a=9...a-c=9~1
a=8a-c=8~1

a=1a-c=1
99*(1*9+2*8+3*7+4*6+5*5+6*4+7*3+8*2+9*1)=16335
ͤϡξ¤ǡξƱȹͤ16335*2ȹͤΤǤ
褯ͤ
줾(A,C)Ȥ˴ؤơ¤09ޤǤ10̤ꤺĹͤ뤫
٤ƤΣ£äξκ¤Ȥʤ
16335*2*1032670ȤʤΤǤ礦
ʤߤʤ󡢴ְ㤤Τʤδְ㤤õΤ褦ʽ񤭹ߤǤߤޤ󡣡
731ڡ 16:11:50 42143
uchinyan
#42143Mr.ǥ¾
ʸɤѹΤ褯ʬʤΤDzȤޤ󤬡
n = ABC = 000 999 Τ٤ƤФ m = CBA ͤ |n - m| ¤ΤʤС
326700 Ǥ礦
ͥνȡ 731ڡ 16:46:04 MAIL:uchi@sco.bekkoame.ne.jp 42144
ޤ륱
ˣ׻Ƥߤޤ
ñˡ飹οФƵդοĤꡢ
λݣ׻ϢǤοͤ¸
Ϣ˻ĤäιפɽƤߤޤ
̡ȤͤȤʤꡢʥޥޤμǤη̤Ȱۤʤޤ

Ĵ٤̡ʥޥޤμǤϡ
ʣݣġˡߣܡʣ¡ݣáˡߣ
ΥθƤ餺
ʣݣġˡߣݡʣ¡ݣáˡߣʣݣġˡߣʣ¡ݣáˡߣ
ΥϳƤ뤻Ȼפޤ

ȡξʬϤäʣˤʤꡢäȰ̲񤷤ʵޤ
äƤˤ̵Ǥ

ʤߤˡޤǤη׻̤򤵤餷ޤ

405
4455
858195
8593695
1633065705
16330920705
3102880348395
ʤ硡 731ڡ 17:30:00 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42145
ޤ륱
äȲɤơ15ޤ

405
4455
858195
8593695
1633065705
16330920705
3102880348395
31028808898395
5895473797619505
58954738083119505
11201400237864770595
112014002380719770595
21282660452376530641305
212826604523805080641305
ʤ硡 731ڡ 18:07:40 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42146
Mr.ǥ
#42144 uchinyanͭ񤦤ޤ(ޤϰ¿
>16335*2*1032670ȤʤΤǤ礦פ
16335*2*10326700ȤʤΤǤ礦פǤ
ʲ򤦤ƤΤǤ礦͡ʾСˡ
731ڡ 19:23:59 42147
ޤ륱
̵ɤϡäƤߤʤ狼ʤ

((10^(n-(i*2-1))-1) * 10^(i-1)) * 45 * 19^(floor(n/2)-i), i = 1, floor(n/2)
ʤ硡 731ڡ 19:24:57 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42148
ޤ륱
rubyΥץdzǧޤ
ץफؤäݤľ˴ְ㤤⤰ꤳǤǽ⤢Τǡ
ǧץŽդޤ

ʤߤˡʲѥڡȤäƤΤǡԥڤƼ¹Ԥϥڡʤ꥿֤ʤ֤Ƥ

#!/usr/bin/ruby

def solv(n)
total = 0
(1..(n/2).to_i).each do |i|
total += ((10**(n-(i*2-1))-1) * 10**(i-1)) * 45 * 19**((n/2).to_i-i)
end
return total
end

(2..15).each do |n|
p solv(n)
end

ʤ硡 731ڡ 19:28:52 HomePage:ޤ륱42149
uchinyan
#42145
ޤ륱󤵤
äȤΤ褦Ǥ͡
äꤷޤ

Jޥޤ
åøǤ
ʤ
ͥνȡ 731ڡ 20:19:06 MAIL:uchi@sco.bekkoame.ne.jp 42150

#42145
ޤ륱󤵤
ä̤Ǥ͡
ΩƤŤƷ餱ǤѤ(>_<)

#42150
ȤǤʤǤ
Ȥ⤴ƳǤ
731ڡ 22:14:49 42151

|ABC-CBA|=|(A0C+0B0)-(C0A+0B0)|=|A0C-C0A|
=|100*(A-C)+(C-A)|=|99*A-99*C|=99*|A-C|
|A-C|ȹͤΤ0,1,2,...,8,9
99*(1+2+...+9)=4455
3Τޤޤη׻̤Ȼפä̵Ǥ
731ڡ 22:48:30 42152
⡼ޥ
#42143 Mr.ǥ ^^
錄ϡޤ㤵Τ褦˹ͤޤǤ ^^;
褯ʬʤʤäƤޤޤOrz...
¨ ^^;v 731ڡ 22:56:00 42153

#42148

N=2ġ459
N=3ġ4599
N=4ġ45(99919+90)
N=5ġ45(999919+990)
N=6ġ45(999991919+999019+900)
N=7ġ45(9999991919+9999019+9900)
N=8ġ45(9999999191919+9999901919+9990019+9000)


Ȥ
NΤȤġ45ߦ{k=1toN/2}[{10^(N-k)-10^(k-1)}19^(N/2-k)]
NΤȤġ45ߦ{k=1to(N-1)/2}[{10^(N-k)-10^(k-1)}19^{(N-1)/2-k}]

Ǥ礦ġ
եդޤ

ץϤޤäɤޤ󤬡̤򸫤ʤͤޤm(__)m

731ڡ 23:54:36 42154
ޤ
äޤġ

100A+10B+C ǹͤϤơ
326700,16335 ǧڤǤϤ줿ȡ
ʸɤľơ
(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) * 99 = 45 * 99 = 4455
ˤäȵŤޤ orz
somewhere in the world 81ʶ 2:47:01 42155

001,002,003,004,005,006,007,008,009Ĵ٤Ʋ򤭤ޤ
81ʶ 3:11:53 HomePage:42156
ޤ륱
饤ʡ
ruby -e 'n=3;p (1..(n/2)).map{|i|((10**(n-(i*2-1))-1)*10**(i-1))*45*19**((n/2)-i)}.inject(:+)'
ʤ硡 81ʶ 10:50:40 MAIL:take4310@mobile.email.ne.jp HomePage:ޤ륱42157
uchinyan
#42154#42148
Jޥޤ
#42154η̤ϡ [ ][x] x ĶʤȤȡޤȤơ
45ߦ{k=1to[N/2]}[{10^(N-k)-10^(k-1)}19^([N/2]-k)]
Ƚ񤱤ޤƤϡ
{k=1to[N/2]}[{10^(N-(2k-1))1}10^(k-1)4519^([N/2]-k)]
ѷǤޤ

ǡޤ륱󤵤#42148
((10^(n-(i*2-1))-1) * 10^(i-1)) * 45 * 19^(floor(n/2)-i), i = 1, floor(n/2)
ϡfloor ؿȸƤФΤǥץȤ߹ߴؿȤƤ褯Ȥޤ
floor(n/2) = [n/2] ȻפäƤΤǡJޥޤη̤ƱǤ

ޤ륱󤵤ϥץdzǧƤ褦Ǥ
ޤꤢƤˤʤʤǤ (^^;䤬ǧϰϤǤ⡤ƱˤʤäΤǡ
٤Ȼפޤ
ͥνȡ 81ʶ 14:23:55 MAIL:uchi@sco.bekkoame.ne.jp 42158

#42158
uchinyan

꤬Ȥޤ(*^^*)
ʤۤɡѷȤμ׻䤹Ǥ͡
ϡޤȤʤƤʤΤǤ
ͤƤ꾯ΤǤǼ䤷ޤ
0.5=0-0.5=-1-1.5=-2
ǹäƤޤ(^-^;οˤʤäƤۤʤǤΤǤ礦(^-^;

ޤ륱󤵤Τͤǰ̲Τ餷뤳Ȥ
Ǥޤ
Ȥ꤬Ȥޤ(*^^*)

81ʶ 15:25:27 42159
uchinyan
#42159
0.5=0-0.5=-1-1.5=-2
ǹäƤޤ(^-^;οˤʤäƤۤʤǤΤǤ礦(^-^;
ϤǤ
ͥνȡ 81ʶ 16:09:15 MAIL:uchi@sco.bekkoame.ne.jp 42160

#42160
꤬Ȥޤ(*^^*)
åꤷޤ
81ʶ 16:16:52 42161
Mr.ǥ
⡼ޥ󤵤
uchinyanüŪˡn = ABC = 000 999 Τ٤ƤФ m = CBA
ͤ |n - m| ¡פȽ񤤤ƤΤǤ
ȡ㤨СA>CȤϸ¤ʤΤ
[ABC]743ΤȤؤΤȤκϡ99*|7-3|=396
[ABC]347ΤȤؤΤȤκ⡡99*|3-7|=396
錄ϡΣĤȤäƤȹͤޤ2
82ڡ 8:31:31 42162
???
VBSCRIPT
dim p(999)
for j=0 to 999:p(j)=0:next
for A=0 to 9:for B=0 to 9:for C=0 to 9
p(abs((100*A+10*B+C)-(100*C+10*B+A)))=1
next:next:next
wa=0:for j=0 to 999:wa=wa+j*p(j):next
msgbox wa
82ڡ 8:41:14 42163