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Question of the day. palindromes
Old 03-21-2013, 10:28 PM   #1
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Default Question of the day. palindromes

A palindrome is a word, sentence, or number that reads the same from left to right as from right to left.

Examples of palindromes.

Radar.
Rotor.
Dad.
Nun. and so on.. number now.
414.
35653.

the question now.
How many palindromes possible with 3 numbers?

For Cale and over.
How many palindromes possible with 351 numbers?
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Old 03-21-2013, 11:29 PM   #2
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100

10^176
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Old 03-22-2013, 12:14 AM   #3
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42

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Old 03-22-2013, 01:02 AM   #4
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Old 03-22-2013, 06:01 AM   #5
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We will wait for our chief of maths.

PS: Bard and Govi are making fun of this serious thread...
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Old 03-22-2013, 06:09 AM   #6
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In the main time, here is the John Nash movie..

http://www.imdb.com/title/tt0268978/
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Old 03-22-2013, 10:36 AM   #7
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Old 03-22-2013, 11:00 AM   #8
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Quote:
Originally Posted by Tout View Post
We will wait for our chief of maths.

PS: Bard and Govi are making fun of this serious thread...
Not so, in my case. Again:

3 digit palindromes number 100

351 digit palindromes number 10^176 (10 to the 176th power).
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Old 03-22-2013, 12:49 PM   #9
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Me? Yes, I was making fun.

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Old 03-22-2013, 12:54 PM   #10
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Old 03-22-2013, 01:57 PM   #11
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Quote:
Originally Posted by Govi View Post
Not so, in my case. Again:

3 digit palindromes number 100

351 digit palindromes number 10^176 (10 to the 176th power).

Sorry but 3 digit palindromes are not 100!
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Old 03-22-2013, 02:06 PM   #12
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Tip.

we have just 9 palindromes with 2 numbers!
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Old 03-22-2013, 02:09 PM   #13
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You mean 3 digit numbers ONLY? In other words, excluding single and two digit numbers.

101, 111, 121, 131, 141, 151, 161, 171, 181, 191 - There 10.
Across 9 sets (100's, 200's, 300's, 400's, 500's, 600's, 700's, 800's, 900's).

There are 90 (10*9). For numbers that ONLY contain 3 digits.

If you are including two digit numbers, there are 9 of those.
11, 22, 33, 44, 55, 66, 77, 88, 99 since 00 is actually a single digit number.

I don't believe there are any single digits which constitute a palindrome unless they all count.

Which means:
3 Digits - 90
2 Digits - 9
1 Digit - 0

So, 99 is the the number of palindromes between {0,999}
90 is the number of palindromes between {100,999}
9 is the number of palindromes between {0,99}

Edit to add: Apparently all single digit numbers are palindromes, so, add 10 to that, and we have 109.

Last edited by Textured Surface; 03-22-2013 at 02:50 PM.
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Old 03-22-2013, 02:12 PM   #14
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Tout smiles, bravo.
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Old 03-22-2013, 02:23 PM   #15
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According to this, all single digit numbers are palindromes, so it is actually 109.
In other words, all single digit numbers are technically palindromes.
There are 10 of them (0 through 9).

So, 109.
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Old 03-22-2013, 02:26 PM   #16
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Palindromes can be considered as numbers mirrors. There are pairs and odd, respectively 2.n and who 2.n + 1 digit. And 351 is impair ( odd)
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Old 03-22-2013, 02:27 PM   #17
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Based on that, the number of palindromes formed by all numbers, from 0 up to and including all numbers with 351 digits in them are as follows:

10 followed by 350/2 9's

or, 10 followed by 175 9's

The sequence is, if it is odd it is preceded by 10.
It is followed by n, minus 1, divided by 2, number of 9's

If you want to discount single digits from being palindromes, deduct 10 from that number.
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Old 03-22-2013, 02:31 PM   #18
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Note that the first can not be null. 01 is the same as one, right? Otherwise it would not be in the game!
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Old 03-22-2013, 02:33 PM   #19
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They are counting 1, 2, 3, 4, etc... as palindromes.
I don't know why, intuitively, it would seem that a single digit number wasn't a palindrome.

Like I said, just deduct 10 from the number 10, followed by 175 9's if you don't want them counted.

If you are just looking for the number of palindromes formed by numbers with exactly 351 digits it is

10, followed by 175 9's
minus
1 followed by 175 9's
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Old 03-22-2013, 02:34 PM   #20
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I just nerded out.
Post tits please.
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Old 03-22-2013, 02:42 PM   #21
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You are hot.....
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Old 03-22-2013, 02:52 PM   #22
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Quote:
Originally Posted by Textured Surface View Post
I just nerded out.
Post tits please.

Okey...Made.


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Old 03-23-2013, 06:39 PM   #23
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Ok, here we are.

We determine the number of palindromic numbers 351 = 9x10 ^ numbers is 175 (nine, ten power 175 because 351 = 2x175 +1) 2)
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Old 03-23-2013, 07:00 PM   #24
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lol
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Old 03-23-2013, 07:03 PM   #25
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You're missing some palindromes.

odd digited palindromes are of the form

aNe, where a and e are the mirror of each other and N = 0, 1, 2,...9

For a 351 digited palindrome, if a (and e) are any number in the set [0, (10^175)-1], then the number of palindromes of the form aNe is 10 x 10^175 or 10^176.
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Old 03-23-2013, 07:05 PM   #26
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Quote:
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lol
madam!
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Old 03-23-2013, 07:10 PM   #27
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Ooooh wait! I have another one!

lolololololol
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Old 03-23-2013, 07:12 PM   #28
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Quote:
Originally Posted by Govi View Post
You're missing some palindromes.

odd digited palindromes are of the form

aNe, where a and e are the mirror of each other and N = 0, 1, 2,...9

For a 351 digited palindrome, if a (and e) are any number in the set [0, (10^175)-1], then the number of palindromes of the form aNe is 10 x 10^175 or 10^176.

The leftmost digit of the group before the pivot can only take values ​​from 1 to 9 (there is no number starting with zero)
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Old 03-23-2013, 07:14 PM   #29
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Quote:
Originally Posted by GradyE View Post
Ooooh wait! I have another one!

lolololololol

Never ever even
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Old 03-23-2013, 07:27 PM   #30
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Well we need a referee now.........where is our chief?
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Old 03-23-2013, 07:28 PM   #31
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Quote:
Originally Posted by Tout View Post
The leftmost digit of the group before the pivot can only take values ​​from 1 to 9 (there is no number starting with zero)
You have brought that rule in at the end. This is how you began:

Quote:
Originally Posted by Tout View Post
A palindrome is a word, sentence, or number that reads the same from left to right as from right to left.

Examples of palindromes.

Radar.
Rotor.
Dad.
Nun. and so on.. number now.
414.
35653.

the question now.
How many palindromes possible with 3 numbers?

For Cale and over.
How many palindromes possible with 351 numbers?
All numbers have an infinity of leading zeroes; we just don't write them because of practicality and convention. 001 is the same thing as 1. <sigh> And in the digital world within our computers, the only way of writing 1 is 00000000000000000000000000000000000000000000000000 0000000000000001 (that should be 63 leading zeros, for a 64 bit machine.) (If you count them, you're one up on me in analness.)
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Old 03-23-2013, 07:32 PM   #32
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<sigh> too...

9x10 puissance 175. And that is all.

Last edited by Tout; 03-29-2013 at 06:12 PM.
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Old 03-24-2013, 12:31 PM   #33
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You are hot.....
Too hot to hoot?
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