Three Digit Palindromes
What is the smallest three digit palindrome divisible by 18? Can you solve this without a brute force examination of possibilities?
Communicated by Tom Chiari.
What is the smallest three digit palindrome divisible by 18? Can you solve this without a brute force examination of possibilities?
Communicated by Tom Chiari.
To: [email protected]
To: [email protected]
To: [email protected]
To: [email protected]
To: [email protected]
To: [email protected]
To A. N. Shanbhag
several people have solved; I don’t post the answers (you are supposed to email me, but if you can’t you can post and I just don’t
approve) as I don’t want to spoil people’s fun
well done
[[your email did not work]]
nice, but there is a solution when you interpret it the way most children would, namely divisible means it goes in a whole number of times and
leaves a remainder of zero.
It’s 101 because it says divisible but not that it has to be an integer.
It’s 101 because it says divisible, but not that it has to be an integer
PS I’m a child
No, less.
414
anon — yes — [email protected]
yes (sjm1 AT williams.edu)
Rage: correct
Thanks — normally the word divisible implies no remainder. /s
you might want to consider adding the demand that the outcome is a natural number as well… in it’s current form, the correct answer is 101 🙂
(101 / 18 = 5 11/18 tadaa 😉 )
Ravi: yes — please email at sjm1 AT williams.edu as I don’t like to post answers
glad you’re enjoying it: sjm1 AT williams.edu
coll tnx!
I’m removing your post as you have the correct answer, but yes, please use in your math class and let me know how it goes (sjm1 AT williams.edu). I’m happy to have your students, if they do well, appear in the hall of fame.
sent hint //s
Can you please email the answer?i like to be ur fb frnd.pls give me ur fb id
sure //s
Can you please email the answer?
it has to be an integer, yes. not sure what you mean by product; the number must be a palindrome and a multiple of 18.
Does the three digit number’s product have to be 18 and a whole number?
something smaller works ..s
414
not sure where you’re getting 333 from — that’s not the answer. //s
Still trying to figure out how 333 works … unless we’re using some unconventional definition of “divisible by” or “18” …
Ah, nice thinking! We want the smallest positive one…. :]
-828? Does that count as a palindrome?
xiaomilk: correct, not posting as it’s the soln
nope — not three digits, and not divisible by 2.
99
Anonymous: correct!
252
Unfortuantely not, as 108 isn’t a palindrome.
is it 108?
people typically don’t consider that a 3 digit number, so look a bit higher (you’re on the right track)….
Is the answer 090? If not, may I have the correct answer? thank you!
no a smaller works. //s (email me at [email protected] for the soln)
so the awnser is 333????????
Rob: correct, well done! Not posting as it’s the soln.
while 666 works, something smaller works as well…. //s
Is it 666?
sure — shoot me an email at [email protected]
I know! May I “spill the beans” as it were?