About Sangaku

”Sangaku” is a unique Japanese approach
for learning.

Originally, it refers to wooden tablets with Japanese mathematical problems, presented as offerings to Shinto shrines and Buddhist temples. This culture is said to be peculiar to Japan. Although most problems are difficult, ”Sangaku” has long been popular among Japanese people as a custom of expressing gratitude to Gods or Buddha for the joy of being able to solve a problem and praying for scholarly accomplishment.

Submitting your Entries

How to Submit

Please fill out the required items in the form provided for each problem, attach your solutions and submit.

Submission Deadline

The deadline for submitting your solutions is 1 p.m. on July 31, 2017 (Monday).
Application for submitting answers has been closed.

Best Solutions

The best solutions will be shown on this website on September 1, 2017 (Friday).


Those who solve the problems well will receive an original book-gift card worth 5,000 yen from The Mathematics Certification Institute of Japan.


These problems can be solved in more than one way. It is important to show how you think and solve the problems.

Problems for 2017

Question 1 for 2017

The fingers of the Great Buddha at Todaiji Temple are webbed. This is said to have two meanings. First, it signifies that the Great Buddha overcame hard training. Second, it means that he rescues everyone without letting anyone slip through his fingers. The problem is, if the Great Buddha were to scoop up water in his both hands, how much water (in liters) could he hold?


One way to solve this problem could be to compare the size of the Great Buddha′s hand with the size of a human hand. If you use your hands for the comparison, you could actually scoop up some water in your hands and check the amount before working on the problem.

Problem 2 for 2017

Japan has an ancient traditional culture of appreciating the aromas of a natural fragrant wood. This art is called “Kodo” (the way of incense). In “Kodo”, smelling an incense is expressed as kiku (to listen). “Kodo” is said to comprise two main elements – “monko” (written with Chinese characters meaning “to listen” and “fragrance”) and “kumiko” (written with Chinese characters meaning “to combine” and “fragrance”). “Monko” means listening to and appreciating the aromas of a fragrant wood, whereas “kumiko” is a game of telling one fragrance from another. It is believed that every fragrant wood is a living creature with a soul. It is thought that we must respect and take great care of scarce natural fragrant woods, be thankful for the blessings of nature and the earth, and listen to what the woods have to say. “Ranjatai” is a piece of natural fragrant wood considered to have the finest incense on earth. It is kept in the Shosoin Repository (currently managed by the Imperial Household Agency) of Todaiji Temple. The image below shows facts known about “Ranjatai”. How much is its average density based on the length and weight measurements given?

“Ranjatai” is the special, tasteful name given to this piece of wood. This name comprises three Chinese characters which have the characters for Todaiji() hidden inside them.