Question

Rina, while waiting for her friend Tina, started playing with matchsticks. By the time Tina reached, she made the figure “$262226$” using the matchsticks. Tina accidentally steps on the pattern and all the matchsticks got spread all over. Rina was upset with this and wanted to find the number of matchsticks she wasted?

• A. $21$
• B. $26$
• C. $32$
• D. $36$

Answer 1

The correct option is C

$32$

From the image above, we see that $5$ matchsticks are required to make $2and6$ matchsticks are needed to make $6$.
So if the number of 2's is taken as '$a$' and the number of sixes is taken as '$b$'.
The number of matchsticks needed to make the 2's $=5\times a=5a$
The number of matchsticks needed to make the 6's $=6\times b=6b$
Total number of matchsticks $=5a+6b$
In the number $262226$, there are $4$ '$2$'s and $2$ '$6$'s.
Hence, $a=4$ and $b=2$

Therefore, the total number of matches required $=5a+6b=5\times 4+6\times 2$
$=20+12=32$