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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Guest Message by DevFuse

Started by Molly Mae, Sep 30 2011 08:00 PM

6 replies to this topic

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?

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.**

Posted 30 September 2011 - 08:22 PM

Spoiler for first effort

Posted 30 September 2011 - 08:25 PM

Think I'm missing overlaps, but someone else can expand if I did.

Posted 30 September 2011 - 08:33 PM

Good enough for me.Spoiler for first effort

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

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

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 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

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:

Posted 03 October 2011 - 03:06 PM

Right, I wasn't asking for the minimum, else it would have strictly been 6. Which is also not clever.Spoiler for Hmmm ... Aren't we all missing something?

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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