Page 2066 of 2379

Re: Count to a Million

Posted: Sun May 20, 2018 10:30 pm UTC
by addams
82601
Another Century!

Aww! Crap!
Tree??
Image
Whine...! Why wasn't it MaMa Bear!

Re: Count to a Million

Posted: Sun May 20, 2018 10:43 pm UTC
by cyanyoshi
82602

There's always the next page-topper! Let's hurry!

Re: Count to a Million

Posted: Sun May 20, 2018 10:59 pm UTC
by addams
82603
Okay!

Re: Count to a Million

Posted: Sun May 20, 2018 11:10 pm UTC
by cyanyoshi
82604

Re: Count to a Million

Posted: Sun May 20, 2018 11:16 pm UTC
by addams
82605

Re: Count to a Million

Posted: Sun May 20, 2018 11:22 pm UTC
by cyanyoshi
82606

Re: Count to a Million

Posted: Sun May 20, 2018 11:28 pm UTC
by addams
82607
We'll be there in No Time.

Re: Count to a Million

Posted: Sun May 20, 2018 11:48 pm UTC
by cyanyoshi
82608

Re: Count to a Million

Posted: Sun May 20, 2018 11:57 pm UTC
by Seven
82609

Re: Count to a Million

Posted: Sun May 20, 2018 11:58 pm UTC
by cyanyoshi
82610

Re: Count to a Million

Posted: Sun May 20, 2018 11:59 pm UTC
by addams
82611

Re: Count to a Million

Posted: Mon May 21, 2018 12:00 am UTC
by cyanyoshi
82612

Re: Count to a Million

Posted: Mon May 21, 2018 12:03 am UTC
by Seven
82613

cyanyoshi wrote:There are 900 six-digit palindromes, since there are 9 choices for the first digit (1-9), and ten choices for the second and third digits. The last three digits are uniquely determined from the first three. As for the rest of the five-digit numbers, there’s 82628, 82728, … 99899, and 99999. So the number of five digit palindromes left to go is 999-826+1=174.

All in all, there are 1074 more palindromes left until a million.
This is cool to know! Thanks!

Re: Count to a Million

Posted: Mon May 21, 2018 12:20 am UTC
by addams
82614
Seven!
Do you understand Why?

Re: Count to a Million

Posted: Mon May 21, 2018 3:25 am UTC
by Seven
82615

Do I understand why what?

Re: Count to a Million

Posted: Mon May 21, 2018 3:27 am UTC
by addams
82616
Why the number of Palindrome is so low.

Re: Count to a Million

Posted: Mon May 21, 2018 3:30 am UTC
by Seven
82617
fix'd
Oh, yes. Yes I do.

Re: Count to a Million

Posted: Mon May 21, 2018 4:01 am UTC
by addams
82618
So funny.
You are Thinking so hard, you forgot to count!

Re: Count to a Million

Posted: Mon May 21, 2018 4:04 am UTC
by Seven
82619

:shock: Oops! I thought I had... *thinks even harder*

I meant to, anyway! LOL

Re: Count to a Million

Posted: Mon May 21, 2018 4:14 am UTC
by ObsessoMom
82620

My calculations are, as usual, less elegant than cyanyoshi's, but they provide another way of looking at why palindromes become less frequent as we approach one million:

Spoiler:
The single-digit numbers were all palindromes: 1, 2, 3, ..., 7, 8, 9. There were 9 of those, rather than 10, because 0 couldn't be used as a single digit in counting.
The two-digit numbers had one palindrome per decade: 11, 22, 33, ..., 77, 88, 99. There were 9 of those, rather than 10, because 0 couldn't be used as an initial digit in counting.
The three-digit numbers also had one palindrome per decade. 101, 111, 121, ..., 979, 989, 999. There were 10 of those for each of the 9 possible starting digits, because 0 could now start to appear in palindromes (as a middle digit). 10 x 9 = 90.
The four-digit numbers had one palindrome per century: 1001, 1111, 1221, ..., 9779, 9889, 9999. There were 10 of those for each of the 9 possible starting digits, because 0 could be used as a middle digit. 10 x 9 = 90.
The five-digit numbers also had/will have one palindrome per century: 10001, 10101, 10201, ..., 99799, 99899, 99999). There have been/will be 100 of those for each of the 9 possible starting digits. 100 x 9 = 900.
The six-digit numbers will have one palindrome per millennium (100001, 101101, 102201, ...997799, 998899, 999999). There will be 100 of those for each of the 9 possible starting digits. 100 x 9 = 900.

Total palindromes between 1 and 1000000 = 9 + 9 + 90 + 90 + 900 + 900 = 1998.
Total palindromes already encountered (i.e., between 1 and 82628) = 9 + 9 + 90 + 90 + 726 = 924
Total palindromes yet to go (i.e., between 82728 and 1000000) = 174 + 900 = 1074

Re: Count to a Million

Posted: Mon May 21, 2018 4:45 am UTC
by addams
82621
*Bows deeply*
It's so nice to have you around.

Re: Count to a Million

Posted: Mon May 21, 2018 4:58 am UTC
by ObsessoMom
82622

Re: Count to a Million

Posted: Mon May 21, 2018 5:00 am UTC
by addams
82623
Your explanation was easy to follow.
Yoshi's was a valid proof!

Re: Count to a Million

Posted: Mon May 21, 2018 5:20 am UTC
by flicky1991
82624

Speaking of palindromes... incoming in 4. :D

Re: Count to a Million

Posted: Mon May 21, 2018 5:34 am UTC
by addams
82625
You are Up!

Re: Count to a Million

Posted: Mon May 21, 2018 5:35 am UTC
by Seven
82626

Re: Count to a Million

Posted: Mon May 21, 2018 5:43 am UTC
by flicky1991
82627

Next poster is one lucky poster.

Re: Count to a Million

Posted: Mon May 21, 2018 5:50 am UTC
by Seven
82628

It me

Re: Count to a Million

Posted: Mon May 21, 2018 6:13 am UTC
by addams
82629
Seven is a Lucky Number!

Re: Count to a Million

Posted: Mon May 21, 2018 6:13 am UTC
by addams
82630
Seven is a Lucky Number!

Oops a Glitch in the Tubes.
We must hurry off this page.

Re: Count to a Million

Posted: Mon May 21, 2018 6:53 am UTC
by flicky1991
82631

No worries, addams.

Re: Count to a Million

Posted: Mon May 21, 2018 6:58 am UTC
by addams
82632
Tanks Birdie.

Re: Count to a Million

Posted: Mon May 21, 2018 7:24 am UTC
by Seven
82633

Re: Count to a Million

Posted: Mon May 21, 2018 9:05 am UTC
by addams
82634

Re: Count to a Million

Posted: Mon May 21, 2018 12:33 pm UTC
by flicky1991
82635

Re: Count to a Million

Posted: Mon May 21, 2018 12:34 pm UTC
by Earthling on Mars
82636

Re: Count to a Million

Posted: Mon May 21, 2018 12:35 pm UTC
by flicky1991
82637

Re: Count to a Million

Posted: Mon May 21, 2018 1:04 pm UTC
by addams
82638

Re: Count to a Million

Posted: Mon May 21, 2018 1:05 pm UTC
by flicky1991
82639

Re: Count to a Million

Posted: Mon May 21, 2018 3:01 pm UTC
by cyanyoshi
82640