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

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## #1 2010-03-20 22:45:06

JaneFairfax
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### Cute little problem I saw on another site

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

## #2 2010-03-20 23:00:19

mathsyperson
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### 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.

## #3 2010-03-23 17:37:04

scientia
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### 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,

## #4 2010-05-07 05:54:09

JaneFairfax
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### 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 ∊ Mn

Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?