perplexus.info :: Numbers : 2 3 1 2 1 3

2 3 1 2 1 3 (Posted on 2004-11-23)

If two 1's, two 2's and two 3's are arranged thus:

2 3 1 2 1 3

then the two 1's enclose 1 other digit, the two 2's enclose 2 other digits, and the two 3's enclose 3 other digits.

Can you find a similar arrangement using the seven pairs 1,1,...7,7?

Submitted by Erik O.

Rating: 4.2857 (7 votes)

Solution: (Hide)

The following program, written in some flavor of BASIC, provides the solutions given below...
10 dim Z(14)
20 for A=1 to 12
30 One1=A:One2=A+2
40 for B=1 to 11
50 Two1=B:Two2=B+3
60 for C=1 to 10
70 Three1=C:Three2=C+4
80 for D=1 to 9
90 Four1=D:Four2=D+5
100 for E=1 to 8
110 Five1=E:Five2=E+6
120 for F=1 to 7
130 Six1=F:Six2=F+7
140 for G=1 to 6
150 Seven1=G:Seven2=G+8
160 Z(One1)=1:Z(One2)=1
170 Z(Two1)=2:Z(Two2)=2
180 Z(Three1)=3:Z(Three2)=3
190 Z(Four1)=4:Z(Four2)=4
200 Z(Five1)=5:Z(Five2)=5
210 Z(Six1)=6:Z(Six2)=6
220 Z(Seven1)=7:Z(Seven2)=7
230 for X=1 to 14
240 if Z(X)=0 then Flag=1
250 next X
260 if Flag=1 then goto 290
270 Flag=0
280 for X=1 to 14:print Z(X);:next X:print
290 Flag=0
300 for X=1 to 14:Z(X)=0:next X
310 next G
320 next F
330 next E
340 next D
350 next C
360 next B
370 next A
1 7 1 2 5 6 2 3 4 7 5 3 6 4
1 7 1 2 6 4 2 5 3 7 4 6 3 5
1 6 1 7 2 4 5 2 6 3 4 7 5 3
1 5 1 6 7 2 4 5 2 3 6 4 7 3
1 4 1 5 6 7 4 2 3 5 2 6 3 7
1 4 1 6 7 3 4 5 2 3 6 2 7 5
1 6 1 3 5 7 4 3 6 2 5 4 2 7
1 5 1 7 3 4 6 5 3 2 4 7 2 6
1 5 1 6 3 7 4 5 3 2 6 4 2 7
1 5 1 4 6 7 3 5 4 2 3 6 2 7
5 1 7 1 6 2 5 4 2 3 7 6 4 3
4 1 7 1 6 4 2 5 3 2 7 6 3 5
4 1 6 1 7 4 3 5 2 6 3 2 7 5
7 1 3 1 6 4 3 5 7 2 4 6 2 5
7 1 4 1 6 3 5 4 7 3 2 6 5 2
6 1 5 1 7 3 4 6 5 3 2 4 7 2
4 6 1 7 1 4 5 2 6 3 2 7 5 3
7 3 1 6 1 3 4 5 7 2 6 4 2 5
4 6 1 7 1 4 3 5 6 2 3 7 2 5
5 6 1 7 1 3 5 4 6 3 2 7 4 2
7 4 1 5 1 6 4 3 7 5 2 3 6 2
5 7 1 4 1 6 5 3 4 7 2 3 6 2
3 6 7 1 3 1 4 5 6 2 7 4 2 5
5 7 4 1 6 1 5 4 3 7 2 6 3 2
2 6 7 2 1 5 1 4 6 3 7 5 4 3
4 5 6 7 1 4 1 5 3 6 2 7 3 2
2 3 7 2 6 3 5 1 4 1 7 6 5 4
3 4 5 7 3 6 4 1 5 1 2 7 6 2
2 3 6 2 7 3 4 5 1 6 1 4 7 5
5 2 4 7 2 6 5 4 1 3 1 7 6 3
2 6 3 2 7 4 3 5 6 1 4 1 7 5
2 6 3 2 5 7 3 4 6 1 5 1 4 7
2 4 7 2 3 6 4 5 3 1 7 1 6 5
5 2 7 3 2 6 5 3 4 1 7 1 6 4
5 2 4 6 2 7 5 4 3 1 6 1 3 7
3 5 7 2 3 6 2 5 4 1 7 1 6 4
2 7 4 2 3 5 6 4 3 7 1 5 1 6
2 5 6 2 3 7 4 5 3 6 1 4 1 7
5 2 6 4 2 7 5 3 4 6 1 3 1 7
5 7 2 3 6 2 5 3 4 7 1 6 1 4
5 3 6 7 2 3 5 2 4 6 1 7 1 4
3 4 6 7 3 2 4 5 2 6 1 7 1 5
7 2 6 3 2 4 5 3 7 6 4 1 5 1
7 2 4 6 2 3 5 4 7 3 6 1 5 1
6 2 7 4 2 3 5 6 4 3 7 1 5 1
7 2 4 5 2 6 3 4 7 5 3 1 6 1
5 7 2 6 3 2 5 4 3 7 6 1 4 1
7 3 6 2 5 3 2 4 7 6 5 1 4 1
3 7 4 6 3 2 5 4 2 7 6 1 5 1
3 5 7 4 3 6 2 5 4 2 7 1 6 1
5 3 6 4 7 3 5 2 4 6 2 1 7 1
4 6 3 5 7 4 3 2 6 5 2 1 7 1

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
A possible answer	K Sengupta	2007-11-24 05:46:06
Solution	Michael	2004-11-29 04:42:55
Another solution	Willard	2004-11-27 16:00:33
just 4	sragen	2004-11-27 05:20:31
ha HA!	mamta	2004-11-23 23:04:10
one more level	Charlie	2004-11-23 20:33:12
spoiler	SilverKnight	2004-11-23 20:30:50
computer solution (spoiler)	Charlie	2004-11-23 20:29:25
I got 6!	Danny	2004-11-23 19:53:37
Well I got 4!	Danny	2004-11-23 19:44:08

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