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

You are welcome to solve one or two problems.
Please do send in your solutions.

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 10, 2020 (Tursday).

Best Solutions

The best solutions will be published on this website on November 2020.


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

Problems for 2020

Problem 1 for 2020

The last step in the construction of the Great Buddha was a ceremony called Kaigenkuyoe (“offering of the opened eyes”), in which the eyes were painted on and the Buddha’s spirit was invited into the statue. The completion of the Great Buddha at Todai-ji was celebrated on the ninth day of April in the fourth year of Tenpyo Shoho (CE 752), the day this ceremony was held.
In the time between the Kaigenkuyoe and today, upon how many worshippers has the Great Buddha cast his eyes?

                        to Submission Form

Problem 2 for 2020

The construction of the Nandaimon (South Gate) and the Nio guardian statues inside was completed in the third year of Kennin (CE 1203).
The Nandaimon is 25.46 meters high and 28.78 meters across, making it one of the country’s largest temple gates. Using 18 pillars, each standing 21 meters high, it is known for its solid construction.
The Nio guardian statues are one of the country’s largest wooden statues, standing at a height of 8.38 meters and weighing 6.68 tons.
How many tons does the Nandaimon weigh?

                        to Submission Form