Question

Caesar and Brutus are playing a game in which each says the next number from a well-known sequence. the first 20 terms of the sequence are given below:

1 2 3 2 1 2 3 4 2 1 2 3 4 3 2 3 4 5 3 2

The fortieth term is 2. if Caesar began the game who will be the first to say 10?

Answer 1

Want me to tell you how i got it?

Answer 2

sure !!!!

Answer 3

wait a little please...

Answer 4

Ok

Answer 5

if you want a hint let me know :)

Answer 6

Roman numeral representation - Brutus?

Answer 7

Your onto something

Answer 8

Put answer in chat so you dont kill it for every one els

Answer 9

"1 2 3 2 1 2 3 4 2 1 2 3 4 3 2 3 4 5 3 2 ... " - Number of letters in Roman numeral representation of n

Answer 10

Ok i typed my answer Let me know when hoblos

Answer 11

Good Job @FoolForMath

Answer 12

he does not have it yet

Answer 13

He gave it out now it computation

Answer 14

There is still more to it but we will see.. let me know when i can drop the answer

Answer 15

Once you find out there are roman numerals are involved in the series you can find out the series is generated by counting the number of characters in the corresponding roman numeral as you can see for the first ten numbers below:

I II III IV V VI VII VII IX X
1 2 3 2 1 2 3 4 2 1

The first term to equal 10 is the 288th in the series: CCLXXXVIII Thus the answer to the question is Brutus

Answer 16

Yeah so ?

Answer 17

Yea he did get it Great job Foolformath

Answer 18

How you find 288? mentally?!

Answer 19

My approach, I used mathematica:

a[n_] := StringLength[IntegerString[n, "Roman"]];
n = 100; While[a[n ] != 10, n = n + 1];Print[n]

Answer 20

now, if n is odd then Caesar says else Brutus.

Answer 21

Interesting approach man

Answer 22

Hey don't throw medals just because i appriciated

Answer 23

That is not interesting, I am just being lazy :P

Answer 24

Cant really describe how I came up with the answer at first i thought I failed but then i start to write it on paper and it was like a flash

Answer 25

kinda hurt my head to much to keep track of with out paper :\

Answer 26

any of you try to do it in your head?

Answer 27

I don't have a head.

Answer 28

oh noz :P anway im off to sleep i have geometry and for some reason i can do this in my head BUT no not geometry :(

Answer 29

Anyway Goodnight i might post some more later after i get some geometry homework done today, sad part is i have to get up at 10 am and its 5 am now :(