Answers to the problem of arranging matches into squares
Many students, after discovering the matching rule, solved the problem of arranging matches into squares of 5th graders.
Threads:
Alex constructs different squares with matches of equal length according to a general rule and numbered 1, 2, 3,… for the squares as shown in the figure below.
How many more matches are needed to make the 1111th square to become the 2022th square?
Solution:
Notice that the nth square has n(n+1) matches horizontally and n(n+1) matches vertically, that is, there are 2n(n+1) matches in all. Thence inferred:
The number of matches in the 1111th square is: 2 x 1111 x (1111 + 1) = 2470864 (sticks).
The number of matches in the 2022 square is: 2 x 2022 x (2022 + 1) = 8181012 (sticks).
So, in order to arrange the 1111th square to the 2022th square, we have the number of matches we need to add: 8181012 – 2470864 = 5710148 (matchstick).
Answer: 5710148 (matchstick).
Tran Phuong
at Blogtuan.info – Source: vnexpress.net – Read the original article here
