Chapter 1.2, Problem 43HP

To determine

To write: two different rulesthat relate the figure number to the number of toothpicks

Answer to Problem 43HP

The number of toothpicks in that figure is given by $2n+4$ and $2\left(n+2\right)$ .

Explanation of Solution

Given:

  

Calculation:

Looking at the picture showing the terms, count the number of toothpicks for any term and form the following table.

figure number	Number of toothpicks
1	6
2	8
3	10

Now, look at the above table, find a relation between term number and number of toothpicks as shown below:

Figure number	Number of toothpicks
1	$2\times 1+4=6$
2	$2\times 2+4=8$
3	$2\times 3+4=10$

Thus relation can be defined as:

Let n be the figure number,

Then the number of toothpicks in that figure is given by $2n+4$ .

This relation can be explained by top multiplied by two to give the top and bottom, than add 4 for the slopped sides.

Now, another relation between term number and number of toothpicks is as shown below:

Figure number	Number of toothpicks
1	$2\left(1+2\right)=6$
2	$2\left(2+2\right)=8$
3	$2\left(3+2\right)=10$

Thus relation can be defined as:

Let n be the figure number,

Then the number of toothpicks in that figure is given by $2\left(n+2\right)$ .

This relation can be explained by that the bracket term represents half of the figure and then multiplied by two to get the complete figure.

Conclusion:

Thus, the number of toothpicks in that figure is given by $2n+4$ and $2\left(n+2\right)$ .