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6 replies to this topic

### #1 Molly Mae

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Posted 30 September 2011 - 08:00 PM

So pi never repeats, eh?

Assume that an arbitrary number extends into infinity without ever repeating in whole.

Tell me: what is the number of digits needed to guarantee that any string of 5 numbers is repeated?

Edited by Molly Mae, 30 September 2011 - 08:07 PM.

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### #2 maurice

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Posted 30 September 2011 - 08:22 PM

Spoiler for first effort

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### #3 maurice

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Posted 30 September 2011 - 08:25 PM

Think I'm missing overlaps, but someone else can expand if I did.
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### #4 Molly Mae

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Posted 30 September 2011 - 08:33 PM

Spoiler for first effort

Good enough for me.

Now: What if no number can ever appear twice in a row?
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### #5 thoughtfulfellow

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Posted 01 October 2011 - 06:07 AM

I see two interpretations for Molly Mae's additional restriction "Now: What if no number can ever appear twice in a row?" Assuming that you mean that the irrational number never has two of the same digit in a row, then
Spoiler for Solution for original and limitation as I interpreted it above

On the other hand, if the intent is to allow the irrational number to have same digits adjacent but find a repeating sequence that does not allow adjacent numbers
Spoiler for THEN

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### #6 Gihan

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Posted 02 October 2011 - 01:43 PM

Spoiler for Hmmm ... Aren't we all missing something?

Spoiler for Here's my answer to the variation:

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### #7 Molly Mae

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Posted 03 October 2011 - 03:06 PM

Spoiler for Hmmm ... Aren't we all missing something?

Right, I wasn't asking for the minimum, else it would have strictly been 6. Which is also not clever.

My wording was simple and straightforward for two reasons: If pi extends into infinity, can we ever anticipate a string of 5 numbers to repeat? 10 numbers? 12,462 numbers?

EDIT: (The second reason is that I was bored on a Friday...which happens often where I am.)

Spoiler for Here's my answer to the variation:

Edited by Molly Mae, 03 October 2011 - 03:07 PM.

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