Question

What is the next number in this sequence: 2210, 2201, 2120, 2102, 2012, ?

Answer 1

is the answer 1994?

Answer 2

No. Hint: this finite sequence is made up of 4-digit numbers consisting of only the digits 0,1,2, and 2.

Answer 3

2109 ,2019

Answer 4

I thought it like this. The difference between the first two numbers is 9(2201-2210), and then the difference the next two numbers is 81(2201-2120).
Then the difference between the next two numbers is 18(=9*2)(2120-2102) and the difference between the next two numbers is 81 again. (2021-2102)
Thus the difference between the next two numbers should be 9*3=27., So 2021-27=1994.
I cant understand why this should be wrong!

Answer 5

is it 2021?

Answer 6

Let me cogitate on your explanation. Some sequences can have more than just one unique "next term."

I got 2012 because I thought the values of the numbers were decreasing and I was supposed to use just the digits 2, 2, 1, and 0.

Answer 7

so who is right?

Answer 8

I'm still cogitating. Mani defended his answer so I'm thinking his answer may be correct. 2012 is the "suggested" correct answer but that doesn't mean it is the only correct answer.

Answer 9

I see

Answer 10

Do you have a "defense" for your answer? That would help me in my cogitations.

Answer 11

My?

Answer 12

Well I made up a pattern ...

Answer 13

i think directrix is right...2012...u see that in the following no.s the last two digits change their places....

Answer 14

But I know i'm wrong

Answer 15

It's 2021. Am I right?

Answer 16

Well actually the last number given in the sequence is 2021(see the attachment). Directrix has mistyped the sequence

Answer 17

Oh sorry. Then it shud b 2012

Answer 18

Majority wins, I guess. Your answer seems much more logical too, Directrix. But if you can find any reason why my method was wrong, please tell me