EG
äǤ͡ǤȤޤ
졼ϽĴǤ礦
ĤԤڤߤˤƤޤ
72ڡ 0:15:14 49301
٥륯åĥ
оμʳ϶ˤʤƤϤʤΤǡоμˤϴġ
7Ĥξ1̤ꡣ
5Ĥ֤76221̤ꡢĤä4ޥΤʳ֤1̤ʤΤ21121̤ꡣ
3Ĥ765635̤ꡢĤä16ޥξʤ֤3̤ꡢ˻Ĥä4ޥ1̤ʤΤ3531105̤ꡣ
1Ĥȡ7531105̤ꡣ
232̤ˤʤޤ
72ڡ 0:17:15 49302
Ȥʤ
̤〜
оݼˤθĿ(1,3,5,7)ǾʬơоݼˤʤΥڥκͤ롣
72ڡ 0:17:29 49303
٥륯åĥ
Ȥʤ󤪤ǤȤޤ

ߥƤ餱ƤޤޤޤޤȤ­ʤ褦Ǥ
72ڡ 0:18:42 49304
algebra
7C1537C337C51105105211232(̤)
72ڡ 0:37:49 49305
䡼
nnΤȤδݤνA(n)ȤȡA(1)=1,A(2)=2,A(3)=4,A(4)=10ȤʤäΤǡŪA(n)=(n-1)A(n-2)+A(n-1)ͽۤǤޤμΰ̣狼鶵Ƥ
72ڡ 0:50:49 49306
ǯ
Ф357ĤξǰƤơɤ105ǥʤΤǺǤޤ
7C1*5*3+7C3*3+7C5*1+7C7232
72ڡ 0:57:24 49307
baLLjugglermoka
ͤȲˡƱǤ͡105+105+21+1=232¤ϻȥڥȤ鷺˰ŻDz򤭤ޤ(^^)
72ڡ 1:00:32 49308
鯤ο
mmгnĤˤʤοAm,nȤȡ

A2,01
A4,03*A2,03
A6,05*A4,015

A7,0=0
A7,1=7C1*A6,0105
A7,20
A7,3=7C3*A4,0105
A7,40
A7,5=7C5*A2,021
A7,60
A7,71

פơ105+105+21+1232
//

m=7ξϡгʳ˶ĤȤ顢гˤϴġ
Ȥϡгˡ1ġ3ġ5֤˾ʬȡ
줾ξϡ
гؤ֤7Cn̤Τ줾Фơ
Ĥζ֤ϡг֤ޥνIJʤ(m-n)*(m-n)ξ
г֤ʤο뤫顢嵭Τ褦ʷ̤ˤʤ롣
72ڡ 1:10:41 49309
Mr.ǥ
ब1⤺魯ȤξɽȤ󤬤ޤबΤȹͤޤʤΤȤгˡޤ
7बȤ..........1̤
5बȤ...ϡ7C521̤
äȹ礻ϡ1̤
3बȤ...ϡ7C335̤
ä4ȹ礻ϡ3̤
1बȤ...ϡ7̤
ä6ȹ礻ϡ(6C2x4C2x2C2)/3!=15(̤)
ä
1+21+353+715232
ʤͤ⤢꤫ʡ
72ڡ 1:16:17 49310
鯤ο
#49309
䤢Ȥϡгˡ1ġ3ġ5֤˾ʬȡ
Ȥϡгˡ1ġ3ġ5ġ7֤˾ʬȡ
72ڡ 1:16:20 49311
鯤ο
#49306

nnΤȤδݤνA(n)ȤȡA(1)=1,A(2)=2,A(3)=4,A(4)=10ȤʤäΤǡ
䤳ŪA(n)=(n-1)A(n-2)+A(n-1)ͽۤǤޤ
䤳μΰ̣狼鶵Ƥ

A(n)(1,1)ˡ֤ȡ(1,1)ˡ֤ʤʬƿ롣

(1,1)ˡ֤οϡ
1ԡ1(n-1)(n-1)ξΡ֤A(n-1)

(1,1)ˡ֤ʤϡ
(1,k)(k,1)2ޥ(k1)֤Ȥˤʤꡢ
Ĥ֤ξοϡ1ԡkԡ1k(n-2)(n-2)ξΡ֤A(n-2)
kμϡ(n-1)̤顢ɡ(1,1)ˡ֤ʤϡ(n-1)A(n-2)Ȥʤ롣

äơ
A(n)=(n-1)A(n-2)+A(n-1)
//
72ڡ 2:33:05 49312
䡼
鯤οͤ󡢾ܤƤꤢ꤬Ȥޤ
1,2,4,10¤ӤפĤμäΤǤʰ̣Ǥ͡
ٶˤʤޤ
72ڡ 5:34:40 49313
䡼ͧ
ͧͤإԥå˽о줷Ƥޤơ
72ڡ 5:56:52 49314
ֿء׾ι
ۤʤ6ĤΤΤ2ĤȤκοְ㤨Ȥߥ򤷤Ƥޤޤ̵ǰǤʡݡݡ
72ڡ 6:16:58 49315
ˤ
гδݤΤĤȤȤ߹碌ͤޤ
Ķļˡ 72ڡ 6:46:15 49316
Ȥ
ޤ˰ʲΤ褦ѿդ

(a01)(a02)(a03)(a04)(a05)(a06)(a07)
(a08)(a09)(a10)(a11)(a12)(a13)(a14)
(a15)(a16)(a17)(a18)(a19)(a20)(a21)
(a22)(a23)(a24)(a25)(a26)(a27)(a28)
(a29)(a30)(a31)(a32)(a33)(a34)(a35)
(a36)(a37)(a38)(a39)(a40)(a41)(a42)
(a43)(a44)(a45)(a46)(a47)(a48)(a49)

֤ʤ0,֥ޥ1ȤƽBasic

print time$
for a1=0 to 1
for a2=0 to 1
for a3=0 to 1
for a4=0 to 1
for a5=0 to 1
for a6=0 to 1
for a7=0 to 1
if a1+a2+a3+a4+a5+a6+a7<>1 then goto 430
for a8=0 to 1
for a9=0 to 1
for a10=0 to 1
for a11=0 to 1
for a12=0 to 1
for a13=0 to 1
for a14=0 to 1
if a8+a9+a10+a11+a12+a13+a14<>1 then goto 360
for a15=0 to 1
for a16=0 to 1
for a17=0 to 1
for a18=0 to 1
for a19=0 to 1
for a20=0 to 1
for a21=0 to 1
if a15+a16+a17+a18+a19+a20+a21<>1 then goto 290
for a22=0 to 1
for a23=0 to 1
for a24=0 to 1
for a25=0 to 1
for a26=0 to 1
for a27=0 to 1
for a28=0 to 1
if a22+a23+a24+a25+a26+a27+a28<>1 then goto 220
for a29=0 to 1
for a30=0 to 1
for a31=0 to 1
for a32=0 to 1
for a33=0 to 1
for a34=0 to 1
for a35=0 to 1
if a29+a30+a31+a32+a33+a34+a35<>1 then goto 150
for a36=0 to 1
for a37=0 to 1
for a38=0 to 1
for a39=0 to 1
for a40=0 to 1
for a41=0 to 1
for a42=0 to 1
if a36+a37+a38+a39+a40+a41+a42<>1 then goto 80
for a43=0 to 1
if a1+a8+a15+a22+a29+a36+a43<>1 then goto 70
for a44=0 to 1
if a2+a9+a16+a23+a30+a37+a44<>1 then goto 60
for a45=0 to 1
if a3+a10+a17+a24+a31+a38+a45<>1 then goto 50
for a46=0 to 1
if a4+a11+a18+a25+a32+a39+a46<>1 then goto 40
for a47=0 to 1
if a5+a12+a19+a26+a33+a40+a47<>1 then goto 30
for a48=0 to 1
if a6+a13+a20+a27+a34+a41+a48<>1 then goto 20
for a49=0 to 1
if a7+a14+a21+a28+a35+a42+a49<>1 or a43+a44+a45+a46+a47+a48+a49<>1 then goto 10
if a2=a8 and a10=a16 and a18=a24 and a26=a32 and a34=a40 and a42=a48 and a3=a15 and a11=a23 and a19=a31 and a27=a39 and a35=a47 and a4=a22 and a12=a30 and a20=a38 and a28=a46 and a5=a29 and a13=a37 and a21=a45 and a6=a36 and a14=a44 and a7=a43 then let s=s+1
10 next a49
20 next a48
30 next a47
40 next a46
50 next a45
60 next a44
70 next a43
80 next a42
90 next a41
100 next a40
110 next a39
120 next a38
130 next a37
140 next a36
150 next a35
160 next a34
170 next a33
180 next a32
190 next a31
200 next a30
210 next a29
220 next a28
230 next a27
240 next a26
250 next a25
260 next a24
270 next a23
280 next a22
290 next a21
300 next a20
310 next a19
320 next a18
330 next a17
340 next a16
350 next a15
360 next a14
370 next a13
380 next a12
390 next a11
400 next a10
410 next a9
420 next a8
430 next a7
440 next a6
450 next a5
460 next a4
470 next a3
480 next a2
490 next a1
print s
print time$
end

f9
09:47:03
232()
09:47:06
˭ԡ 72ڡ 9:48:35 MAIL:fttnm528@ybb.ne.jp 49317
̻
Ȥ߹碌ꡣĥޤ
褦ʹͤǵޤ

1+7C2+(7C2*5C2)/2+(7C2*5C2*3C2)/(2*3)=1+21+105+105=232

72ڡ 12:33:11 49318
SECOND
! BASIC ׻232 ̤ǽФޤ
! a(1)a(7) ̣(ź)򡢹Ԥ()ˡбơa(a(N))=N гоΡ

DIM a(8)
MAT READ a
DATA 1,2,3,4,5,6,7,0
CALL perm20(1)

SUB perm20(k)
local i
IF k< 7 THEN
FOR i=k TO 7
swap a(k),a(i)
CALL perm20(k+1)
swap a(k),a(i)
NEXT i !--- ġν P(7,7) ---
ELSEIF a(a(1))=1 AND a(a(2))=2 AND a(a(3))=3 AND a(a(4))=4 AND a(a(5))=5 AND a(a(6))=6 AND a(a(7))=7 THEN
LET a(8)=a(8)+1
MAT PRINT USING "! # # # # # # # No_####" :a
END IF
END SUB

!¹Է̡ ʲ a(1)a(7) ̣(ź)ϡν
! 1 2 3 4 5 6 7 No_ 1
! 1 2 3 4 5 7 6 No_ 2
! 1 2 3 4 6 5 7 No_ 3
! 1 2 3 4 7 6 5 No_ 4
! (
! )
! 7 6 3 5 4 2 1 No_ 230
! 7 6 4 3 5 2 1 No_ 231
! 7 6 5 4 3 2 1 No_ 232
72ڡ 16:27:41 49319
⡼ޥ
3ܤˤƤäȵŤޤ ^^;
֤äƤޤ...
г2Ĺ...ĤĺդΤ...1:1б
so...
c(7,0)+c(7,2)+c(7,2)*c(5,2)/2!+c(7,2)*c(5,2)*c(3,2)/3!
=232

ǤΤ͢
/2!, /3! ˵ŤƤޤǤ...^^;;
72ڡ 17:18:42 49320
鯤ο
#49313

nǵưѤ뵤ΤǡñȤ1Τơ˶2Ĥ1An,BnǴطΤơǸ2Am,n򲼤˷׻ƤˡDz򤤤Τǡäꡢ1Σ򼨤ơ줿Ȼפޤ
1,2,4,10Ƚ񤭤ƤɡϻפĤޤǤ
A8ޤǸڤä顢ͤƤߤ顢Ϥޤޤ
ص塢Ȥ򤷤Ƥ뤬ǡͤѥžѤǤߤι⹻ؤǤϡ򶵤ʤʤäƤ뤽顢ͤˤä⤷ޤ
72ڡ 17:58:03 49321
ϺĹ
how many hours I have stopped at 105ġ
72ڡ 20:09:00 49322
ˤ⡼
ץ˿夲

гˡȤǤʤοǾʬ

ʣг󤬣ġ̤ꡡĭ

ʣг󣵤ġĤ21̤
ĤꣲĤоΤˤʤ̤ꡡ
21ߣ21̤ĭ

ʣг󣳤ġĤ35̤
ĤꣴĤоΤˤʤ
ĤΣĤ£ãĤȤȡߤоΤˤʤȤ
ʣ,ãġˡʣ,£ġˡʣ,£áˤΣ̤ꡡ
35ߣ105̤ĭ

ʣг󣱤ġĤ̤
ĤꣶĤоΤˤʤ
Ĥ£ãģţƤȤ
Ȥ̤ˡ줾ĤꣴΥڥȤ̤
ߣ15̤

ģ15105̤ĭ
ܭܭܭ232̤
¡ 72ڡ 23:19:26 HomePage:˥ͥäΥڡ49323
CRYING DOLPHIN
䡼϶줷ġ
⤽ˤζ̳ľޤǾ12򤹤ФƤơ
77Ф7֤оΤˤʤͤϲ̤ꡩפȤ
ʣ٤ˤ󤦤ӹäƤΤǤ

򤷤ƤϤʴ
nnˡ̤nĤФоΤ֤οS(n)ɽޤ㤨кǤ






͢S(7)

Ф֤ͤޤ
־β֤Фг֤ݤǾʬޤ
ޤФ֤ʤʤäϡߤɽޤ
ߡߡߡߡߡ
ߡ
ߡ
ߡ
ߡ
ߡ
ߡ͢S(6)

ߡߡߡߡߡ
ߡߡߡߡߡ
ߡߡ
ߡߡ
ߡߡ
ߡߡ
ߡߡ͢S(5)

ߡߡߡߡߡ
ߡߡ
ߡߡߡߡߡߡ
ߡߡ
ߡߡ
ߡߡ
ߡߡ͢S(5)







ͤ͢٤S(5)

Ȥ櫓ǡS(7)S(6)6S(5)ɽޤ






͢S(6)

ߡߡߡߡ
ߡ
ߡ
ߡ
ߡ
ߡ͢S(5)

ߡߡߡߡ
ߡߡߡߡ
ߡߡ
ߡߡ
ߡߡ
ߡߡ͢S(4)

ߡߡߡߡ
ߡߡ
ߡߡߡߡߡ
ߡߡ
ߡߡ
ߡߡ͢S(4)






ͤ͢٤S(4)

Ȥ櫓ǡS(6)S(5)5S(4)ɽޤ

Ʊͤ˹ͤơ
S(5)S(4)4S(3)
S(4)S(3)3S(2)
S(3)S(2)2S(1)
Ȥʤꡢ
S(1)1̤ꡢ

S(2)2̤ꤢΤǡ
ߡߡ
ߡ
S(3)4S(4)10S(5)26S(6)76S(7)232Ƚ缡ޤޤ
夲ƻ衡 73ʶ 8:43:23 MAIL:Ԥ HomePage:ԤԤ󤹤49324
CRYING DOLPHIN
ࡢߤˤϤʤΤ
ǤʤΤǤҤȤޤΤޤޤǢ||_
夲ƻ衡 73ʶ 8:51:47 MAIL:Ԥ HomePage:ԤԤ󤹤49325
SECOND
! 5 7 3 4 1 6 2 No_ 177
! 1 2 3 4 5 6 7
!
! ʴǡNo_ 1 No_ 232
! Ϣ³ץȡʲ򽽿BASC ǣá
!
!
!
!

DIM a(8), w70$(7, 0 TO 7), w7$(7, 0 TO 7)
MAT READ a, w70$
DATA 1,2,3,4,5,6,7,0
DATA "! ",,,,,,,
DATA "! ",,,,,,,
DATA "! ",,,,,,,
DATA "! ",,,,,,,
DATA "! ",,,,,,,
DATA "! ",,,,,,,
DATA "! ",,,,,,,
CALL perm20(1)

SUB perm20(k)
local i
IF k< 7 THEN
FOR i=k TO 7
swap a(k),a(i)
CALL perm20(k+1)
swap a(k),a(i)
NEXT i !--- ġν P(7,7) ---
ELSEIF a(a(1))=1 AND a(a(2))=2 AND a(a(3))=3 AND a(a(4))=4 AND a(a(5))=5 AND a(a(6))=6 AND a(a(7))=7 THEN
LET a(8)=a(8)+1
CALL pattern2
END IF
END SUB

SUB pattern2
MAT PRINT USING "! # # # # # # # No_####" :a
PRINT "! 1 2 3 4 5 6 7"
MAT w7$=w70$
FOR x=1 TO 7
LET w7$(a(x),x)=""
NEXT x
MAT PRINT w7$;
END SUB
74ڡ 2:24:37 49326
Ф
г1ġ3ġ5ġ7ĤǾʬޤ
76C24C21/3!+7C34C21/27C2+1232
74ڡ 4:32:11 MAIL:hbmath1965@yahoo.co.jp 49327
Ф
ʤΤɤǤ礦

̤Ĺ6Ĺ12ξߤͤ
̤Ǥ
74ڡ 4:36:02 MAIL:hbmath1965@yahoo.co.jp 49328
Ȥ
#49328

ߤޤ褯򤤤Ƥ褦äǡ
ǡMathematica ǡ

Product[(4 Cos[j Pi/5]^2+4 Cos[k Pi/7]^2)^(1/4),{j,1,4},{k,1,6}];
N[%]

enterơ281()

θf(m,n)礭äꤹȿͤϤߤǤ
˭ԡ 74ڡ 8:39:56 MAIL:fttnm528@ybb.ne.jp 49329
̴
#49302 ٥륯åĥ
#49310 Mr.ǥ

Ԥο񤷤ʬäƤϤΤǤ
гοǾʬƤ˻餺
塹ȤƤޤޥܤ246Ĥ
äé夭ޤ
ľ˷ǼĤɤߡٶפޤ嵭˷Ǥͤ
ͤˤäǤޤ
꤬Ȥޤ
ٻΤ桡 74ڡ 9:41:21 49330
⡼ޥ
# 19320 ʥ쥹 Orz

г2гˤʤ...ĤĺդΤ...1:1б

...^^;

錄ΤʤǤ...^^;...줬Ȼפɤʤ
74ڡ 9:58:09 49331
⡼ޥ
#49320
Ǥ...^^;;
74ڡ 10:01:00 49332
ֿء׾ι
ץȤȤĤ¤ΤϡɤޤηäդƤ뤫ȤȤǤΩľᤷƻŹΤȡΤʤդꤷƤΤȤǤϷ׻֤κФƤޤ
ϡ飷ޤǤο飲ļФʣꡢ椫飷ȤФоΤʰ֤ΤߤޤǤΤǡģܤ飷ܤޤǤ٤ƤιԤ˻ФäƤΤ򥫥Ȥޤ
ۤܡʤˤηäդˤ餻ˡǤ˺줫Ǥޤ
rubyǤ

n=Array.new
w=Array.new
p k=[1,2,3,4,5,6,7,1,2,3,4,5,6,7].permutation(2).to_a.uniq.combination(7).select{|m|n=[];w=[];m.each{|k|n.push k.rotate;w.push k[0]}; m-n==[]&&[1,2,3,4,5,6,7]-w==[]}.size
76ʷ 12:55:09 49333
ֿء׾ι
̤ˡߣΤȤοФ褦ˤƤߤޤ
h=5ʤդĹ
c=[];1.step(h,1){|s|c.push s}
p (c+c).permutation(2).to_a.uniq.combination(h).select{|m|n=[];w=[];m.each{|k|n.push k.rotate;w.push k[0]}; m-n==[]&&c-w==[]}.size
76ʷ 16:03:40 49334
Ф
#48329Ȥ⤵ǤͷǤ꤬Ȥޤ
[]
ΤĤǤ̼ФƤʤ˽ФƤ⤴ˡ٤ǤϤʤǤ礦
4mߣm1m2mξߤͤˡaNȤȡ
a11a2a11+4=5a3a21+a14+25+4+2=11
a4a31+a24+a12+311+20+2+3=36
a5a41+a34+a22+a13+236+44+10+3+295
a6a51a44a32a23a12+3
95+144+22+15+2+3281
77ʲС 5:44:54 MAIL:hbmath1965@yahoo.co.jp 49335

ʤǤ礦
715ʿ 23:46:09 49337