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## #1 2005-11-08 04:38:53

Sven
Guest

### Cannot freeken get this one!

THe puzzle is this:

When is half of 13 equal 8?   (Hint: different number system)

I have tried this one with different bases (Base 3 Base 5 etc) and in Hex and Octal...I am either missig something or I am way off track.

Anyone get this?

## #2 2005-11-08 04:44:31

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Cannot freeken get this one!

Hmm. In base x, 13 would be x + 3 (we have base 10, so 13 is 10 + 3), which means that your thing would be (x + 3)/2 = 8.
Shifting the 2 gives x + 3 = 16, so the base is 13.

Why did the vector cross the road?
It wanted to be normal.

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## #3 2005-11-08 05:07:37

Sven
Guest

### Re: Cannot freeken get this one!

I understand the basics there in that equation. HOwever, maybe I am just overthinking:

But is not 13 in base 13 = 1?

That being the case, how can the answer be Half of 13 in base 13 is 8?

## #4 2005-11-08 05:12:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Cannot freeken get this one!

No. 10 in base 10 isn't 1. It's 10.

In base 10, numbers are made up of 1's, 10's, 100's, 1000's and so on, because they are 10¹, 10², 10³ and so on.
Base 13 is similar, but it's made up of 13°'s, 13¹'s, 13²'s and so on.

That means that 13 in base 13 is 1*13+3 = 16, half of which is 8.

Why did the vector cross the road?
It wanted to be normal.

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## #5 2005-11-08 05:22:12

Sven
Guest

### Re: Cannot freeken get this one!

Ahh, I WAS overthinking it. Missed the equation meaning.

Problems arise frequently when you are right-brained and tend to see math in visual form.

Yeah....13 in base 13 means one 13 and 3 ones.

I forgot to see it in a columnar format as opposed to a number of a whole.

Yeah, got it. Thanks alot.

COnverting that number to 10 base would give me

13/10=1 R 3
1/10=0 R 1

13.

Gee, sometimes I really need to get that left side to kick in sooner.

## #6 2005-11-08 08:31:57

MathsIsFun
Registered: 2005-01-21
Posts: 7,685

### Re: Cannot freeken get this one!

LOL! And what a great illustration of bases.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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