Question

On a planet mars, a dominant creature, the rap, is nearing extinction. The number of raps born
any year is one more than the (positive) difference between the number born in the previous
year and the number born in the year before that. For example, if 4 raps were born last year
and 2 the year before, 3 would be born this year. If 7 raps were born last year and 10 the year
before, 4 would be born this year.
2 raps were born in the year 2010 and 9 were born in 2011. What is the first year after 2010
2
when just 1 rap will be born? *
2021
2027
w
2019
2023
2022
Other​

Answer 1

In the year 2023, exactly one rap will be born.

Given that the number of raps born in any year will be one more than the positive difference between the number born in the previous year and the year before.

Also given that in 2010, 2 raps were born, and in 2011, 9 were born.

So, we can make a progression series like:

2010- 2

2011- 9

2012- (9-2)+1 = 8

2013- (9-8)+1 = 2

2014- (8-2)+1 = 7

2015- (7-2)+1= 6

2016- (7-6)+1= 2

2017- (6-2)+1= 5

2018- (5-2)+1= 4

2019- (5-4)+1 = 2

2020- (4-2)+1 = 3

2021- (3-2)+1= 2

2022- (3-2)+1 = 2

2023- (2-2)+1 = 1

Therefore, 1 rap will be born in 2023.