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Chinese Foundation of Japanese Math
Problem 4-7 (From chapter 8 of the Suanfa Tong Zong: “Civil Engineer.”) (1) A horse was stolen. The owner found it and begin to chase the thief after the thief had already gone 37 ri. After the owner traveled 145 ri, he learned that the thief was still 23 ri ahead. After how many more ri did the owner catch up with the thief? (2) A number of identical balls are arranged as shown in figure 2.11, where the base contains 7 balls and the top contains 3 balls. How many balls are there in total? (3) As shown in figure 2.12, many identical balls are arranged in a pyramid, whose base is an equilateral triangle with a side of 7 balls. How many balls are there in total? (4) Identical balls are arranged in pyramid, this time where as shown in figure 2.13, the base is a square of side 12 balls. How many balls are there in total?
Figure 2.11. How many balls are in this truncated pyramid?
Figure 2.12. This pyramid has a triangular base with seven balls along each side. How may balls are in the pyramid?
The solution to problem 1 can be found on page 56. The solutions to problems 2–4 are as follows:
(2) The easiest way to do the problem is to count the balls. However, the sum of integers k from 1 to n is given by the famous formula n
∑k = 1
n(n + 1) . 2