I hope you enjoyed this week’s Hidato puzzles. I’m going to explain how to solve the hardest one, since the strategies used will also help you solve the simpler ones.
The aim is to find the path from 1 to the largest number, in this case 85, such that consecutive numbers touch each other.
The first step is to look and see if there are any giveaways.
And there are.
- 2 has to be between 1 and 3.
- 30 has to be adjacent to 29 and 31.
With 2 in place, this means that there is only one place for 4 that will get us to 6.
But what about 5? It could be in either A or B marked below. Either way, the numbers will continue upwards into the hexagons marked with an x. So at least we know the direction out.
One of the most important strategies is to realize that lines cannot cross. For example, we know we have to get from 31 to 42. Can we go above 53 to get there? No! Since that will break the line from 53 to 57. We have to go below 53.
Likewise, the line from 31 to 42 cannot go to the right of 42 since that will cross the line 43 to 53. This means there is only one place for 41, and one place for 40 .
We also know that the line from 43 to 53 must pass through the hexagons marked y. There is only one place now for 39, which means that z is also in the 43-53 line. Let’s look at where we are now:
I’ve also added some other letters in the diagram, which will help us. Let’s return to the bottom half of the puzzle. What could possibly be in F? Well, the nearby segments are:
- 12-23
- 23-26
- 72-81
By trying them out it is clear that F must be in 12-23. Which means that the G’s must also.
Now look at E. Which segment is it in? The only candidates are 62-72, or 12-23. But it cant be in the former, because if it is it breaks the line of 26-29.
We have shown that E, F and the G’s are in 12-23. And there is only one way of filling that segment in:
And the x’s, y’s and z all fall into place:
What about J? It can only be in the segment 49-53 because no other segment will reach it, adn there is only one way to get there.
This means we can fill in 38, 37, and 36 since otherwise these hexagons will be empty and disconnected.
What about K? Again, it can only be in the segment 53-57 and there is only one way to get there.
What about L? The only segment it can be in is 72-81, and there is only one way to fill it in. The puzzle is taking shape nicely now!
We can slide in 24, 25, 27 and 28. And then 70 and 71.
I find it simplifies things to write out the remaining segments:
- 31-36
- 57-62
- 62-70
- 81-85
82 cannot be above 81 because if it does 81-85 will block 62-70. So 82 must be to the right of 81, and the rest of the segment slots in. As does 68 and 69:
This is the endgame. Consider the segment 31-36. It has to go through M, and there are two ways it can do so. One of them, however, leaves N blank with an empty neighbour, meaning it is impossible for another segment to get to N. So we can fill in 31-36 and the rest is straightforward.
If you like Hidato you can play many more of them at hidato.com
I post a puzzle here on a Monday every two weeks. If you like this sort of thing check out my other Guardian blog Adventures in Numberland. You can also check me out on Twitter, Facebook, Google+ and my personal website.
If know of any great puzzles that you would like me to set here, get in touch.
