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.