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. ”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 entries on September 7, 2018 (Friday).

Application for submitting answers has been closed.

Best Solutions

The best solutions will be published on this website on November 2018.


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

Problems for 2018

Problem 1 for 2018

Todaiji Temple is home to Japan’s oldest existing bath house, called the Oyuya (large bath). It is said to have been used by monks and artisans involved in restoring the Great Buddha during the Kamakura period.
The problem is, if the Great Buddha were to sit in the bath up to his shoulders, how many liters of water would be needed for the bath?

Problem 2 for 2018

The temple bell at Todaiji Temple measures 3.86 meters tall, with a diameter of 2.71 meters and a weight of 26.3 tons. The wooden hammer, which is made of zelkova, measures 4.48 meters long, with a diameter of 30 centimeters and a weight of 180 kilograms. If the fittings are included, it weighs a total of 200 kilograms.
Because of its large size, this hanging bell has long been referred to at Todaiji as the Ogane (large bell).
At midnight on January 1, 2018, a group of eight people struck the Ogane as hard as they could. What would be the length of the radius in kilometers that the sound of the bell carried?