Considering only checkpoint values, the possible sequence of checkpoints are:
[a] 1 > 2 > 3 > 4 > 7 > 6 > 5
[b] 1 > 2 > 5 > 6 > 3 > 4 > 7
[c] 1 > 2 > 5 > 6 > 7 > 4 > 3
[d] 1 > 4 > 7 > 6 > 5 > 2 > 3
[e] 1 > 4 > 3 > 2 > 5 > 6 > 7
[f] 1 > 4 > 7 > 6 > 3 > 2 > 5
[g] 1 > 6 > 7 > 4 > 3 > 2 > 5

But the position of the checkpoints in the grid and the requirement that each cell be passed through limits the successful sequences to [a] and [g]. 

There are three routes that are possible for sequence [a]:
[E]>d1(1)>c1>c2>d2>d3>c3>c4(1)>d4>d5>e5(3)>e2(4)>e1>f1 >f6>c6>c5>b5>b3(7)>b1>a1>a2(6)>a5(5)>a6>b6> [X]

[E]>d1(1)>c1>c4(2)>d4>d5>e5(3)>e3>d3>d2>e2(4)>e1>f1>f6>c6>c5>b5>b3(7)>b1>a1>a2(6)>a5(5)>a6>b6>[X]

[E]>d1(1)>d3>c3>c4(2)>d4>d5>e5(3)>e2(4)>e1>f1>f6>c6>c5 >b5>b3(7)>b1>a1>a2(6)>a5(5)>a6>b6>[X]

Two routes are possible for sequence [g]:
[E]>d1(1)>a1>a2(6)>a3>b3(7)>b2>e2(4)>e1>f1>f6>e6>e5(3)>e3>c3>c4(2)>d4>d6>c6>c5>b5>b4>a4>a5(5)>a6>b6>[X]

[E]>d1(1)>a1>a2(6)>a4>b4>b3(7)>b2>e2(4)>e1>f1>f6>e6>e5(3)>e3>c3>c4(2)>d4>d6>c6>c5>a5(5)>a6>b6>[X] 

Edited on April 9, 2012, 7:19 am

Posted by Dej Mar on 2012-04-08 12:10:16