Question

The number of matchsticks that can be used to write 39 in Roman system are:
(a) 8
(b) 9
(c) 3
(d) 6

Answer 1

Hint:For solving this problem, we first try to convert 39 into Roman numeral system. After getting the expression of 39 in terms of Roman numeral system, we can easily predict how many match-sticks are required by observing the picture of the roman number.

Complete step-by-step answer:
In ancient mathematics, one of the popular representations of numbers is Roman numeral system. numbers in this system are represented by a combination of letters from the Latin alphabet. Some of the possible symbols and value associated with the Roman numerals are:
1 - I
5 - V
6 - VI
7 -VII
8 -VIII
9 -IX
10 - X
50 - L
100 - C
500 - D
1000 - M
Now, using the above formulation, we can rewrite 39 as 10 + 10 + 10 + 10 - 1.
In Roman numerals, 39 is XXXIX.
For making one X, we require 2 matchsticks. So, for making four X, 8 matchsticks are used. And another matchstick is used for I. Therefore, total 9 matchsticks are used.
Hence, option (b) is correct.

Note: This problem can be alternatively solved by first writing the Roman numeral corresponding to 39 and then drawing the pictorial representation of the particular Roman numeral. Total number of matchsticks is equal to the total number of lines in representation.