Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2010-03-19 23:45:06

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

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## #2 2010-03-20 00:00:19

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

### Re: Cute little problem I saw on another site

Ah, now I see how this works. Nice puzzle.

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

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## #3 2010-03-22 18:37:04

scientia
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Registered: 2009-11-13
Posts: 224

### Re: Cute little problem I saw on another site

In general, for
, we have

This can be proved by induction. For the inductive step, note that

Hence, for this problem,

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## #4 2010-05-06 07:54:09

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Cute little problem I saw on another site

scientia wrote:

In general, for
, we have

This is a very neat formula. It also proves that if

then −1 ∊ M[sub]n[/sub]

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