I was reading the November 2008 issue of Discover Magazine. I really enjoy this magazine and find it quite interesting, even though many of the concepts they discuss are far beyond my level of education.
Discover has a section titled “Mind Games” where thy list various puzzles etc. This month they focused on the relatively new number puzzle “Hidato”. The idea is to connect all the given numbers with consecutive numbers. Numbers must be adjacent to each other connecting either vertically, diagonally, or horizontally.
One of their puzzles provided this example, and asked how many possible locations are there for the missing #16.
Hidato Puzzle - Click to Enlarge
The very first location I discovered, did not appear in their solutions. They state there are four different possible squares where the #16 can be placed. Ahh, they were wrong. There are at least 5! Here is their answer:
Hidato Puzzle Answers - Click to Enlarge
Here is my 5th solution they didn’t think of!
Hidato Extra Solution
Doesn’t this make me feel smart! (I am not posting this to say “in your face discover” – I actually love the magazine and have a subscription. I just thought, hey, this is something I can write about 🙂 )
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That’s wonderful! I missed that one. Glad you found it. — Scott Kim, Discover Magazine puzzle columnist
While in Montreal last week my sister in law was working through an advanced Games book, tired of constantly winning Sudoku puzzles. Hidato is her current most favorite puzzle challenge.
also they missed
13,14,16,4
12,15, 3,5
11, 2, 9,6
1 ,10, 7,8
@matt
Matt,
No, placing 16 there does not produce a unique solution. There are at least five solutions with 16 there:
14,15,16, 4
12,13, 3, 5
11, 2, 9, 6
1,10, 7, 8
13,15,16, 4
12,14, 3, 5
11, 2, 9, 6
1,10, 7, 8
14,13,16, 4
12,15, 3, 5
11, 2, 9, 6
1,10, 7, 8
13,15,16, 4
14,13, 3, 5
11, 2, 9, 6
1,10, 7, 8
14,15,16, 4
13,12, 3, 5
11, 2, 9, 6
1,10, 7, 8
The point of the puzzle was not to find “unique” solutions, but rather to find how many locations the #16 can be placed. Click on the first image to see the actual writeup. As for the solution from Matt, he is definately correct that the 16 can be placed there.
Good catch that there are other solutions that wind up with the 16 in that location, but that does not make Matt wrong.
I am surprised actually that there were so many missed solutions to the original puzzle.
There’s still another missed solution:
16,13,14,4
12,15,3,5
11,2,9,6
1,10,7,8
There are a couple more ways to put the 16 in the upper left corner. To summarize, there are seven different squares that the 16 can wind up in. There are no more.
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Scott
you dont help people with the puzzle really becaus some people want the answers and you dont give thaty
I am not sure how I could give the answers? Do you mean for all puzzles out there? Perhaps some kind of tool where you enter in numbers and it spits out all possible solutions would be cool, but not really something I have the capability to create
(Or did I miss-understand your comment?)