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Common smart and quick calculation methods

Common smart and quick calculation methods

Common smart and quick calculation methods

[Forward and Inverse Addition] Use the "Forward and Inverse Addition" formula to find the sum of several consecutive numbers. For example, the "Sum of Hundreds" problem, which was done by the famous mathematician Gauss (Germany) as a child, can be calculated as

Common smart and quick calculation methods

So, 1 + 2 + 3 + 4 + ... + 99 + 100

= 101 × 100 ÷ 2

= 5050.

As another example, calculating "3 + 5 + 7 + ......... + 97 + 99 =?" Can be calculated as

Common smart and quick calculation methods

Therefore, 3 + 5 + 7 + …… + 97 + 99 = (99 + 3) × 49 ÷ 2 = 2499.

The idea of this algorithm is the earliest in the book, the "Zhangqiu Jianshu Jing" in ancient China. Zhang Qiujian used this idea to cleverly answer the question of "Women are not good at weaving":

"There are women who are not good at weaving today, reducing their power and being late. Weaving five feet on the first day, weaving one foot on the last day, and weaving crickets on the thirtyth day. How about weaving?

The meaning of the title is: a woman is not good at weaving. The amount of cloth she woven every day is less than the previous day, and the amount of reduction is equal. She woven 5 feet of cloth on the first day and 1 foot on the last day, for a total of 30 days. Ask her how many cloths have been woven?

The solution given by Zhang Qiujian in the "Arithmetic" is:

"And the number of weaving rulers at the beginning and end of the day, half of it, and the number of days we can multiply by the number of weaving, that is." "Answer: two horses and one foot." This solution, expressed in modern formulas, is

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