How many different types of love are there? According to C. S. Lewis there are apparently 4: Storge/Affection, Philia/Friendship, Eros/Romance, and Agape/Charity. Can you hold all this love in your heart at the same time. Hanayama seems to think so. The Huzzle Cast Arrows puzzle has a heart with 4 arrows stuck in it, one for each of the types of love.I attempted this puzzle at last year’s RPP and didn’t have a chance to solve it. I wasn’t planning on getting my own copy, but since I was placing an order with Puzzle Master for the Puzzle-A-Month Challenge , I added it to my basket.
No matter how the arrows are moved around, and it is a pain to get all 4 arrows where you want them in the orientation that you want them, it just doesn’t seem possible to extract them. Do they come out at an angle? Does more than one come out at a time? Is there some kind of coordinate motion required? How can the shape of the cutout in the heart be exploited? These are just some of the typical questions that arise when struggling with this supposedly simple Level 3 Hanayama puzzle. Personally, I’d rate this one at Level 4.
Although files, pliers, and blowtorches may be included in your puzzle solving kit, there is a solution that does not require any force or external tools. When you have figured it out and know what to look for, it’s not that hard to remove and return the arrows from the heart. Once it’s apart, it’s easier to see exactly how it works without all the arrows flopping around. The solution is easily repeatable and you can play Cupid all day to your heart’s content.
What I like the most about this puzzle is that it is a great application of the Reuleaux Triangle. A Reuleaux Triangle is 2D shape that has the same width regardless of its angle of rotation. You can make a Reuleaux Triangle by taking an equilateral triangle (all sides the same length), and using a compass oriented at each point to connect the other 2 points with an arc that has a radius that is equal to the length of the side of the triangle.The heads and tails of the Hanayama arrows appear to be based on Reuleaux Triangles and the opening in the heart with the other arrows in the way is just a wee bit smaller than the width of the Reuleaux Triangle. I leave it to you to figure out how to get past this paradox.
For more information on the Reuleaux Triangle:
ReplyDeletehttp://mathworld.wolfram.com/ReuleauxTriangle.html
It includes a gif of a near-square hole with a specially-designed drill bit based on this triangle. Timely with last week's blog entry for square holes on Sunday!
Cheers. -Tyler.
Thank you for contributing the reference to Reuleaux Triangles. I've also had people mention that they enjoyed watching youtube videos on Reuleaux Triangles after seeing them referenced in this post.
DeleteHmm, I'll have to get a copy of this puzzle. I've seen several previous versions. All the versions I've seen trick you into the false assumption that all the arrows are the same. But I haven't seen a copy with Reuleaux Arrows!
ReplyDeleteAlthough I've seen other versions of this type of puzzle over the years, I've never had the opportunity to play with one until now. I just considered this one a great application of Reuleaux Triangles. You can email me if you need further information. You can find my email address is in the Paris IPP book.
DeleteI had not realized the shape of the arrows - excellent! There is a puzzle box which also uses this shape, the Luddites Mill from Thomas Cummings. Fun and interesting motion. https://boxesandbooze.blogspot.com/2017/02/let-good-times-reuleaux.html?m=1
ReplyDeleteThank you for the reference to the Luddites Mill box as well as the other references that were contained in the blog. They reminded me of a YouTube video I watched years ago of a special drill bit for making square holes that I found fascinating.
DeleteI have now purchased a copy and solved it. Nice version of the "trapped arrows" puzzle but not one of my favorite Hanayamas.
ReplyDeleteI didn't think that this one would be a problem for you since you have other versions of this type of puzzle. It may not be my favorite Hanayama either, but it looks like a good implementation of this type of puzzle and I'm glad that I got it, especially since it utilized Reuleax Triangles. Then again, I like Vortex and a lot of people seem to hate that one.
DeleteI love the reference to the different types of love. Puzzles with a back story always leave an impression.
ReplyDeleteWe aim to please.
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