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February 23rd, 2018, 02:43 AM   #1
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Arithmetic mean

Hey there,

I've got a really tricky one here and any clue would be very much appreciated:

Which is the greatest natural number which has the following characteristic:

Ignoring the first and the last digit of this number, any other digit must be smaller than the arithmetic mean of the previous and following digits.

E.g. 87278 would apply to this (because 14/2 is greater than 2).

Thank you very much in advance
Broccolii

Last edited by skipjack; February 23rd, 2018 at 08:48 AM.
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February 23rd, 2018, 03:50 AM   #2
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Quote:
Originally Posted by broccolii View Post
Hey there,

I've got a really tricky one here and any clue would be very much appreciated:

Which is the greatest natural number which has the following characteristic:

Ignoring the first and the last digit of this number, any other digit must be smaller than the arithmetic mean of the previous and following digits.

E.g. 87278 would apply to this (because 14/2 is greater than 2).
No, it doesn't. The second digit is 7. The arithmetic mean of the other digits is (8+ 2+ 7+ 8)/4= 25/4= 6.25. 7 is not less than that.

If you mean just the one digit previous and the one digit immediately following, (8+ 2)/2= 5 and 7 is not less than that. You appear to be just looking at the "center" digit but you said "any other digit".

Quote:
Thank you very much in advance.
Broccolii

Last edited by skipjack; February 23rd, 2018 at 08:48 AM.
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February 23rd, 2018, 05:41 AM   #3
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True, thanks for letting me know!
Edit: E.g. 878 would apply to this.
Anyway, do you know how to solve that question though?
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February 23rd, 2018, 08:50 AM   #4
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This has already been dealt with here (assuming that "the previous and following" meant "the immediate previous and immediate following").
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