Subscribe to:
Post Comments (Atom)
skip to main |
skip to sidebar
Due Date
Each problem will have a two week deadline. You must blog your answer(s) for this problem by:
Friday, October 23, 2009
Friday, October 23, 2009
RETURN TO HOME PAGE
Stuck?
- Find some palindromes with four digits
- Do you believe my friend?
- What do you want to show?
- Do you believe my friend?
- What do you want to show?
25 comments:
They are. For example 9009 is divisible by 11. Also 8008 is divisible by 11. I think this true because when you add any number that is divisible by 11 it is a even number. this rule also apllies with Palidromes that are 4 digits.
Your friend is correct. I know this because if you take a number like 2332 for example and add the first two digits by the last two digits: 23+32 and find the sum 55. Then you take that number and see if it's divisible by 11. All four digit palindromes are divisible by 11. You can try any one by this method and it'll work! another example is 5775. 57+75=132 132/11=12
PLEASE DON'T COPY MY FORMULA AND PUT IT IN YOUR OWN WORDS! THANKS!
-Iris
4664 and 6446 work.iris is wright
because 4444 44+44=88. bye $$$$$$$$
I think all 4 digit palindromes can be divided by 11 because 1111 can obviously divide by 11, but then i kept dividing with other palindromes it took me a while to do so many but it end up they all are divisible. a few other ex. numbers are: 1331, 3443, 7887, etc. I also think that it's very clever how they can all divide by 11 because usually i don't see numbers that are able to divide by 11.
it even works with zeros ie; 1001 10+01=11 11/11=1
-Iris
emerson.... wwaaaahhhh i said for people not to copy my formula, theres so many can't u find a different one?!
Iris
I think all of them are. For example 4004 is divisible by 11, the answear is 364. So is 2002 exept the answear is 182. I also found that Iris's theory works. I was going to write a theory, exept it is the same as George's so...
PS: who is Ember?
-Sara
Yup your friend IS right. i.e 2002 is divisible by 11 because 20+2=22/11=2
-Josel
P.S
NO IRIS I DID NOT COPY UR ANSWER. I JUST STAYED UP UNTIL 11:00 P.M AT NIGHT TO FIGURE THIS OUT. I REPEAT I JUST STAYED UP UNTIL 11:00 P.M AT NIGHT TO FIGURE THIS OUT. THANK YOU
HI EVERYONE!!!!!!!!!!!!!
Friend is correct.9449 can be divided by 11 so can 2552.1552/11=141. Every four digit palidrome can be divided by 11. not sure why.
Your friend is right. For example 4554 and 1221 are both divisible by 11. Iris is right if you add the first two digits and the last two digits of a four digit number and the result is divisible by 11 ten the number is to. Like in 5555, 55+55=110 ,110/11 is 10.
-leo
6666 is divisible by 11
9999 is also divisible so i believe that your friend is correct.
your freind is correct. I tried 4884-444, 2882-262, 1991-181 etc and they all worked .every pattern listed is correct. there isn't a single pattern left that i can write about.
All even palidromes are divisible by 11.example
55,262,1234321 and so on. I think I now why all four digit palidromes (even odd ones) because one can go into anything and four digit can be divided two. All even digit palidromes can be divided by 11 (odd or even).
copper i'm not sure i understand your method... how do you know how much to subtract each time?
-Iris
It can be correct or not depending on which way you do it. For instance for 1221 if you add all the numbers together like this 1+2+2+1 it never equals a number divisible by 11. But if you add the first 2 digits and the last 2 digits like for 1991: 19+91 you will always get a number divisible by 11.
yes most of them are but i think that all of the four digit palidromes that have 2 of the same number so in other words all 4 digit palidromes. for example 8008 is divisible by 11 and my examples are: 8008/11= 728 and 4004/ 11= 364
I think that your friend is correct. Any 4 digit number that is a palindrome will be divisible by 11. A couple of examples are: (a) 9009 divided by 11 = 819; (b) 9889 divided by 11 = 899. I think this is correct because the above 2 four digit palindrome numbers were chosen at random and the theory holds true.
Your friend is correct. For example, 3443 is divisible by 11, 7557 is divisble by 11, 4444 is divisible by eleven, and so on. It works for some odd reason. I agree with Iris very. I am not going to copy iris because she'll get mad at me. I'll think of some theory soon.
Wow! That's scary.
1001/11=91
1111/11=101
1221/11=111
1331/11=121
1441/11=131
1551/11=141
1661/11=151
1771/11=161
1881/11=171
1991/11=181
2002/11=182
2112/11=192
2222/11=202
2332/11=212
2442/11=222
2552/11=232
2662/11=242
2772/11=252
2882/11=262
2992/11=272
3003/11=273
3113/11=283
3223/11=293
3443/11=313
3553/11=323
3663/11=333
3773/11=343
3883/11=353
3993/11=363
4004/11=364
4114/11=374
4224/11=384
4334/11=394
4444/11=404
4554/11=414
4664/11=424
4774/11=434
4884/11=444
4994/11=454
Well, that proves your friend's point, unless it isn't enough... ... ...
5005/11=455
5115/11=465
5225/11=475
5335/11=485
5445/11=495
5555/11=505
5665/11=515
5775/11=525
5885/11=535
5995/11=545
6006/11=546
6116/11=556
6226/11=566
6336/11=576
6446/11=586
6556/11=596
6666/11=606
6776/11=616
6886/11=626
6996/11=636
You get the point right? Maybe... ... ... ...
7007/11=637
7117/11=647
7227/11=657
7337/11=667
7447/11=677
7557/11=687
7667/11=697
7777/11=707
7887/11=717
7997/11=727
8008/11=728
8118/11=738
8228/11=748
8338/11=758
8448/11=768
8558/11=778
8668/11=788
8778/11=798
8888/11=808
8998/11=818
9009/11=819
9119/11=829
9229/11=839
9339/11=849
9449/11=859
9559/11=869
9669/11=879
9779/11=889
9889/11=899
9999/11=909
I think that's about all the possibilities… … …
Nope, no more.
Some of you (probably all) might think I used a calculator (not saying I didn't) to get all these answers, but did anybody ever say I couldn't?
I have no other theories other than iris's. you add the first to digits to the second two digits and the sum is always divisible by 11.
Hey everyone,
Sorry I took so long! I tried a few numbers, for instance 4554 and 5665. They both work. Palindromes with the same digit four times are always divisible by eleven. You can divide 4554 into 4444 and 0110 then you know that 4444 and 0110 are divisible by 11 so 4554 must be too. For 5665, 5555 and 0110, that works as well. It works for 4664, 4444 and 0220. I also agree with Iris and found that her theory worked. I just realized that my theory only works (the adding one) if the middle two digits are larger then the outer ones. If they are smaller, then you subtract not add. For instance, 6116, 6666-0550 then you find that 6116 is divisible by eleven. As well as 5335, 5555-0220. I also realized that for the same digit thing I wrote earlier it only works for even number of digits.
~*Katty*
no, not all palidromes are divisible by eleven. take 12321/11 for example, the quotion is 1120R1.
Another example is 232/11 where the quotiont is 21R1.
Yes I think that your friend is right. 4554 is divisible by 11. And so is 3223.
3000+200+20+3 = 3003+220 = 11*273+11*20= 11*293=3223
It's so cool this formula actually works.
For 4554 it is 4000+500+50+4=
4004+550=11*364+11*50=11*414=4554
What you do is break up the number into its thousands, hundreds, tens, ones and then add the ones to the thousands and the tens to the hunderds and then add the two numbers you came up with. Then you find the number that 11 needs to be multiplied by, by doing the thousands plus ones number and the hundreds plus tens number divided by eleven and then find that number and multiply it by eleven. Obviously that answer will be the number that you divided by eleven. Then you take the two numbers that you multiplied by eleven and then add them together. That number times eleven is our answer!!!!!!!! This is really cool. So sorry i was late but it took me that long to figure it out! -emily
It works! For example:
3443/11=313
9009/11=819
5225/11=475
I really like iris's way of doing it:
2222,
22+22+44/11=4
-Ben
Post a Comment