Two SPICY Puzzles

Last night I went to the crest movie theater the only movie theater in Seattle that offers $4 movie tickets. Entering the theater my sister nudged me to” live a little ” the problem is I strictly hold myself to a diet, and when I break the diet in my head I’m thinking ” I already broke my diet so to hell with it ” I bought a large soda, a large popcorn and a one-pound bag of candy. What a disaster🤬😖  …. at least Incredibles 2 was fun and entertaining.

Today’s inspiration for my blog post came from staring at my bookshelf

Sacred Mathematics: Japanese Temple Geometry

I’d like to share two mathematical puzzles   The first being The puzzle of the missing dollar. The second a Sagaku Geometrical problem proposed by a 13-year  old Japanese kid the Pythagoras theorem is all that is needed to solve this one. I’m sure over the course of your life someone has shown you an argument that purportedly shows that 1=0  but if you look closely you can usually find the error.I greatly enjoy catching these subtle errors and I hope it’s something you might enjoy as well ….Or at least I hope you enjoy reading. Now at the risk of being called mean-spirited, I will not leave The solutions. I hope you enjoy trying to figure it out by yourself

The missing dollar

Three friends walk into a hotel to rent a room the clerk charges them $30 so they each pay $10 and hand it to the clerk. Now on the way back to his desk the clerk realizes that he has overcharged. He was only supposed to charge them $25 so to rectify the situation he takes $5 and gives it to the Bellboy and tells the Bellboy to return the $5 to these three friends now the Bellboy on his way over thinks himself “hey these  pals don’t know that they have been overcharged so what I’m going to do is take $2 out of the five and put it in my pocket as a tip and hand $3 to the friends ” so he hands the $3 back to them and they split amongst themselves . however, if you think about it each friend has now paid $9 to the hotel and the Bellboy pocketed $2 and if you add everything up 9 + 9+ 9 + 2 =29

So the question is where did the missing dollar go?


Now before I present to you the second problem I’d like to share with you the history behind Sangaku which I found interesting.

During the Edo period, 1603 -1868 Japanese rulers enforced a strict cultural isolation between Japan and the Western World which means there had very little communication between them. One of the most interesting practices that came out as a result of this isolation is the practice of sangaku

learned poeple of all classes ,from farmers to samurai, produced theorems in Euclidean geometry. These theorems appeared as beautifully colored drawings on wooden tablets which were hung under one of the roof in the precincts of a shrine or temple.

The tablet was called a SANGAKU which means a mathematics tablet in Japanese. Many skilled geometers dedicated a SANGAKU in order to thank the god for the discovery of a theorem. The proof of the proposed theorem was rarely given. This was interpreted as a challenge to other geometers, “See if you can prove this.”

the text was copied from here

when people discovered an interesting geometrical math problem they found so insightful that they Associated it with a spiritual value. they would carve it onto a wooden tablet and leave it as an offering at their local shrine.

Below are three sizes of circle: two black, three white, one grey. Four of the circles are inscribed inside a square which together with the other circles is inscribed inside a triangle. Show that the radius of the grey circle is twice that of the black circles.


sangaku problem

The Solutions won’t be found on this post, but if you would like to know the solutions

you can find them by googling  The Missing dollar

and the 3-4-5 triangle by a kid






10 thoughts on “Two SPICY Puzzles

    1. Being a penny pinching rascal 4$ movies feel as good as going into jc penny and searching the 90% off section and finding great deals.
      I’m starting to think the WordPress demographic isn’t interested In solving puzzles 😂
      If I post anything that’s similar to think I might talk about the history of the puzzle and solve the puzzle myself instead.
      Are you planning a spooky Halloween special blog post?

      Liked by 1 person

    1. I had help, my sister that nudged me to “live a little” Helped with the popcorn , and we weren’t able to finish all the candy . 😀
      I hope your studies have been going well Nicole!
      You caught me as I’m typing up my next blog post. 😆

      Liked by 1 person

      1. My studies are…… Going… Not well…. Lol! I never was a “school” kind of person. I have a problem with authority and I automatically hate everything I’m forced to read… But, I’m plugging along. 😂😂 And you SHOULD live a little!… Although, you could have just streaked across the theatre or something. 😉😲😂
        I’ll look forward to checking out your next post!

        Liked by 1 person

      2. my sister is verry much the same , she’s a ” Fuck you dont tell me what to do!” kind of person .junior year in college i told her to use the feynmann method of studying but im not sure she ever listenend to me. She graduated with a degree in athletic training but has failed her accreditation test twice now. I hope 3rd times’ the charm.
        my ideas of living a little are sooo vanilla 😆😆


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s