# Just can't figure it out!

• Nov 13th 2011, 01:12 AM
boerseun
Just can't figure it out!
Doesn't matter what I try I just can't get this one right...

The problem: If you had to repeat a certain word a few hundred times eg. bafana in a single line: bafanabafanabafanabafana...etc. What formula can be used to find out what the 513th (or any other figure)letter will be. The second part to this problem is: How did you figure the formula out?

Thanks
• Nov 13th 2011, 01:49 AM
ymar
Re: Just can't figure it out!
Where in this very long word does "b" appear? It's the first letter, the seventh, the thirteenth... Let's write some more of this sequence:

1,7,13,19,25,31,37,43,49,55,61,67,...

Do you see the pattern? What is the next number?
• Nov 13th 2011, 01:55 AM
earboth
Re: Just can't figure it out!
Quote:

Originally Posted by boerseun
Doesn't matter what I try I just can't get this one right...

The problem: If you had to repeat a certain word a few hundred times eg. bafana in a single line: bafanabafanabafanabafana...etc. What formula can be used to find out what the 513th (or any other figure)letter will be. The second part to this problem is: How did you figure the formula out?

Thanks

1. At all even numbered places there will be an "a". Since 513 is an odd number, ... no "a".

2. All "b"s occur at the places 1, 7, 13, ... that means at $\displaystyle 1+6p\ , \ p\in \mathbb{N}$

Check if p is a natural number in

$\displaystyle 1+6p = 513$

3. All "f"s occur at the places 3,9,15, ... that means at $\displaystyle 3+6k\ , \ k\in \mathbb{N}$

Check if k is a natural number in

$\displaystyle 3+6k = 513$

4. All "n"s occur at the places 5, 11, 17, ... that means at $\displaystyle 5+6m\ , \ m\in \mathbb{N}$

Check if m is a natural number in

$\displaystyle 5+6m = 513$
• Nov 13th 2011, 04:21 AM
HallsofIvy
Re: Just can't figure it out!
"bafana" itself has 6 letters so to find the nth letter in "bafana" repeated the first thing you would do is determine n modulo 6. If n= 513, 6 divides in 513 85 times with remaimder 3. The third letter in "bafana" is "f" so the 513th letter in the repetition is "f".