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 Postage: 1 to N (Posted on 2010-09-02)
A page of postage stamps in a booklet contained 6 stamps from which it was possible to obtain any total value from 1 to the total value of all the stamps on the page by the appropriate selection of one or more orthogonally connected stamps from those laid out in the following manner:

```+-----+-----+-----+
|     |     |     |
|  1  |  2  |  x  |
|     |     |     |
+-----+-----+-----+
|     |     |     |
|  4  |  6  |  y  |
|     |     |     |
+-----+-----+-----+
```

With the numbers chosen, four of the values could be obtained in two different ways each, and the rest could be obtained in only one way each.

Your job is to figure out the numeric values of x and y.

Note that the square portion already given, containing 1, 2, 4 and 6, would, by itself satisfy the mentioned criterion: all the values from 1 to 13 can be achieved as the total of orthogonally connected stamps, such as 1, 2 and 4 to make 7 (the 6 and the 1 are not orthogonally connected, so that would not be allowed).

 See The Solution Submitted by Charlie Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: solution | Comment 3 of 5 |
(In reply to solution by Dej Mar)

Bravo.

Was it analytically solved or comp.-aided?

How do we know that no better , that is higher reaching pairs exist?

Please advise.

 Posted by Ady TZIDON on 2010-09-02 14:26:26
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