China Elementary School Homework: How Tall is The Table?
First Equation: The distance between (the height of the table plus the height of the cat )and (the height of the table minus the hight of the turtle) is 170 centimeters.
Second Equation: The distance between (the height of the table plus the height of the turtle) and (the height of the table minus the height of the cat) is 130 centimeters.
If we formulate it in mathematical language;
a=table
b=cat
c=turtle
(a+b)-(a-c)=170
(a+c)-(a-b)=130
In order to provide both equations, we need to accept that the table and the turtle are the same height.
If we obtain the number 170 when we remove the 2nd parenthesis from the 1st parenthesis, we can start by accepting the result of the 1st parenthesis as 170 and the result of the 2nd parenthesis as 0. In this case, we will need to reveal the length of the elements in the parenthesis. In accordance with our assumption, we must accept the table as 169 cm, the cat as 1 cm and the turtle as 169 cm. It is also possible to determine the numerical value of the elements in this equation to be greater than 170, since the first parenthesis is removed. For example, if we determine the table as 168 cm, the cat as 2 cm and the turtle as 168 cm, we can still obtain the result of the equation, 170. In order to reinforce the logic, if we accept the table as 1 cm, the cat as 169 cm and the turtle as 1 cm, we can still obtain the result of the equation, 170. In each variation, we have to accept that the table and the turtle have the same height.
Proof of contradiction:
When we accept the turtle as the same height as the table, we have to accept that the cat is 170 cm tall. Because the distance from the highest point of the cat on the table to the highest point of the turtle under the table is given as 170. Since the turtle and the table are the same height, the turtle will not be able to extend the distance under the table.
However, in order to satisfy the equation, we had to accept the cat as being less than 170 cm tall.
