How many five digit palindromes are there?

Question

I messed that up and only realized now. Sorry about that. What I meant is "How many five digit palindromic NUMBERS are there?"

Answer 1

Well, if it can start with 0 then:

10 * 10 * 10 * 1 * 1 = 1000

This is using the multiplication rule since in that case each of the first three slots could be any of the digits 0 through 9 but then the last two could only be one possibility to match the opposite in the first two.

Without 0 as a possible start:

9 * 10 * 10 * 1 * 1 = 900

Again using the multiplication rule with 9 possibilties for the first slot, 1 - 9 and then 0 - 9 for the other two and then only one possibilty for the last two for the same reason as above.

Using this method, the first few 5 digit palindromic numbers would be as follows:

10001
10101
10201
10301
...
11011
11111
...
and so on up to
9999

It is important to realize that 00300 is not a five digit palindromic number.

Answer 2

The first digit can be from 1 to 9, the 2nd from 0 to 9, the 3rd from 0 to 9, while the 4th mirrors the 2nd, and 5th mirrors the 1st. So, the total number is:

9 * 10 * 10 = 900

Answer 3

i think there are 900, but i am looking for my source...

http://members.cox.net/mathmistakes/palindromes.htm
Among the 900 5 digit palindromes, 93 are prime

Answer 4

1000

Answer 5

Not sure why this is posted here, but here's all the English 5-letter ones:

* Aeaea – a location in Greek mythology
* Aiaia – variant of Aeaea (q.v.)
* alala – a type of Hawaiian crow
* alula – a structure forming part of a bird's wing
* Anona – a genus of plants
* Ardra – a Hindu goddess
* Arará – a Cuban ethnic group
* arara – a type of Australian cockatoo; also a Brazilian macaw
* Aviva – a girl's name
* Capac – a town in Michigan, USA
* civic – relating to a city
* deked – past tense of to deke, meaning to deceive (especially in ice hockey)
* deled – past tense of to dele, meaning to delete (a passage of text)
* dered – past tense of to dere, an archaic word meaning to harm
* dewed – past tense of to dew, meaning to cover with dew
* dexed – past tense of to dex, meaning to drink robotussin
* Hamah – variant of Hama, a city in Syria
* Igigi – a class of Sumerian gods
* kaiak – variant of kayak
* Kanak – a native of New Caledonia
* kayak – a light Inuit canoe
* Kazak – a member of a people inhabiting the central Asian republic of Kazakhstan; their language
* kelek – a type of raft used in the Middle East
* Kodok – a town in Sudan
* Laval – a city in Quebec, Canada
* level – various common meanings
* Liril – a cosmetic soap popular in India
* madam – a polite form of address for a woman
* minim – a musical note having half the duration of a full note
* Natan – Hebrew form of the name Nathan
* Navan – the administrative capital of Co. Meath, Ireland
* neven – "To name; to mention; to utter. [Obs.]" (definition from Webster's Dictionary, 1913)
* Noyon – a town in France
* Oruro – a city and department in Bolivia
* put-up – deceitful, as in a put-up job
* radar – a method of detecting objects using radio waves (acronym from Radio Detection And Ranging, so it's self-defining too - i. e., the word "bounces back" like a radar signal)
* refer – various common meanings
* rotor – something that rotates
* sagas – plural of saga, a long narrative story
* semes – plural of seme, a linguistic element
* seres – plural of sere, a series of stages of ecological development
* sexes – plural of sex
* shahs – plural of shah, a former name for the king of Iran
* Sinis – variant of Siris (q.v.)
* siris – a type of tree; (with cap.) a figure in Greek mythology
* solos – plural of solo
* stats – contraction of statistics
* stets – third-person present tense of to stet, meaning to indicate that a passage of text should remain unchanged
* stots – third-person present tense of to stot, meaning to leap or bounce
* sulus – plural of sulu, a type of sarong
* Susus – plural of Susu, a member of a West African people
* Tebet – the fourth month of the Jewish civil year
* Tevet – variant of Tebet (q.v.)
* tenet – a belief or principle
* torot – see [2], [3]
* Tumut – a town in New South Wales, Australia
* Xanax – an anti-anxiety drug (trademark)
* xenex – the sword wielded by Xenophon