[Neraphym]

A sequence of terms is formed by following the two rules below:
* If the term is even, divide by 2 to get to the next turn
* If the term is odd, then multiply by 3 then add 1 to get to the next term

If the first number in the series is 12, then what is the sum of the sequence's first 2003 terms?

Black kite goes to the winner.

[Trifang]

uh....1? Just a guess

[Neraphym]

If the first term is twelve and there is no possible way to get a negative number, then how could the sum of them be less than the origional?

[PKing Monkey]

argh a math question a random guess 4

[Killerconvic]

12

[mohsye 2003]

Umm.......let me think..........i hate math...........i just guess 222963

[vietpryde]

2003?

[Neraphym]

Nope, none of you are right. Nobody is going to get this, so I'll give some hints.

If the first number is twelve, you take 12 and divide it by 2. You get 6. 6 is even, so divide that by 2 to get 3. 3 is odd, so multiply by 3 and add 1 to get 16. Keep at it!

[vietpryde]

2. or do you want us to add all the numbers up?

This post has been edited by vietpryde: 15 November 2003 - 07:46 AM

[Neraphym]

add them up

[Goto]

[mohsye 2003]

Ok, another guess 67. I hope there is no limit to guesses

[Neraphym]

Oops, i got ahead of myself. 3 x 3 = 9 then 9 + 1 = 10
10 is even so divide by 2 to get 5. 5 x 3 + 1 = 16. Sorry about that.

[vietpryde]

You want us to add 2003 numbers???

4729

This post has been edited by vietpryde: 15 November 2003 - 05:07 PM

[Neraphym]

You're off by 10, but I'll give it to ya.

Answer: 4719

12 is even so divide by 2 to get 6
6 is even so divide by 2 to get 3
3 is odd so multiply by 3 and add 1 to get 10
10 is even so divide be 2 to get 5
5 is odd so multiply by 3 and add 1 to get 16
16 is even so divide by 2 to get 8
8 is even so divide by 2 to get 4
4 is even so divide by 2 to get 2
2 is even so divide by 2 to get 1
1 is odd so multiply by 3 then add 1 to get 4
4 is even so divide by 2 to get 2
2 is even so divide by 2 to get 1
1 is odd so multiply by 3 then add 1 to get 4
4 is even so divide by 2 to get 2
2 is even so divide by 2 to get 1
1 is odd so multiply by 3 then add 1 to get 4
4 is even so divide by 2 to get 2
2 is even so divide by 2 to get 1
1 is odd so multiply by 3 then add 1 to get 4...

As you can see, this will go on forever.

To get the sum of the first 2003 terms, we need to take the sume of the first unrepeated terms. (12 + 6 + 3 + 10 + 5 + 16 + 8 = 60) There are 7 of these terms so subtract 7 from 2003 to get 1996. Now the next 1996 terms will consist of 4's, 2's, and 1's. There are 3 of these repeating terms, so divide 1996 by 3. The number you get is 665 and 1/3. Since 4 is the first of the repeating terms, that 1/3 will be a 4. Now add those 3 repeating terms together. (4 + 2 + 1 = 7) Take that 7 and multiply it by 665, and then add 4 because of the extra term. The answer will come out to be 4659. (4655 + 4) Then add the sum of the first terms (60) to that number to get 4719.

Vietpryde figured this out, just he messed up somewhere. It happens. The kite goes to him! Congrats, now for an even harder one!

(I had it written down somewhere, but I lost it. I'll post the next one when I find it.)