31, 3, 5, 11, 23, 13
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.
Transform the following numbers into a palindromic sequence (one that reads the same backwards as forwards) by applying the same formula to all the numbers. What is the formula and what are the resulting numbers?
31, 3, 5, 11, 23, 13
Answer
Square each number to get the palindrome:
961, 9, 25, 121, 529, 169
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Comments
mollynoodl
Jul 25, 2002
 Actually, 3 squared is not 9!! 
SkEwL_gUrl
Jul 26, 2002
 Actually, 3 squared is 9 
george1978
Jul 29, 2002
 yes 3 squared is 9 check your calculator 3x3= 9. for a square of a nuber is a number times it self two times ie 3x3. 
Stargirl
Jul 29, 2002
 that was a really hard one 
sillywilly
Jul 31, 2002
 The key is to identify them as prime numbers. If you pair them in a colums, then you can see the pattern if you're familiar with the squares of primes. 
hcleong
Aug 14, 2002
 Er... multiply each number by 0? 
A_n_d_y
Aug 14, 2002
 no hcleong, the 2 and 5 would mess that idea up. Although it's interesting that it's nearly a palindrome. 
zangel3000
Aug 14, 2002
 No offense, but I don't think that teaser is that great, but hey, but that's just my oppinion. 
Lyceum_
Aug 14, 2002
 Multiplying by zero does work, and the palindrome becomes 0 0 0 0 0 0. You could also say "for every number equal to 5, subtract 3". That would give the sequence 31 3 2 11 23 13. 
bearppbj
Aug 14, 2002
 We have a bunch of brainiacs here. One can't multiply 3 times 3, another can't multiply numbers by 0 and yet another can't spell numbers. I've had a long day, so I'm a bit cranky. 
bearppbj
Aug 14, 2002
 Lyceum, the teaser says to apply the same formula to ALL the numbers, not SOME of the numbers. 
dsquared
Aug 15, 2002
 Great teaser, very clever, very tough. 
mpeoples
Aug 15, 2002
 Multiply each number by zero. It creates a series of zeroes which obviously read that same forward and backward. It's a trick but it's valid. 
majd
Aug 18, 2002
 I guessed it rather quickly, nice one. 
klopper
Sep 09, 2002
 LOL AT MOLLYNOODL 
dsquared
Sep 10, 2002
 Another possibility is to divide each number by itself... another boring answer I know, but it works.... 1,1,1,1,1,1. Just needs a reword to remove these possibilities. It would be good if teasers could be reworded and resubmitted, it would allow for the improvement of many of the teasers on the site. Do you know if this has this been suggested anywhere before Para? 
jimbo
Oct 29, 2003
 Excellent puzzle. Extremely interesting to see the relationships generated between primes, squares and palindromes. A lot of concepts happening here. Thanks! 
griphook
Oct 29, 2003
 only a 3.09 difficulty rating ? extremely difficult but very creative 
vbfreak55
Jul 03, 2004
 i thought this one was very hard. it was a great idea, though! 
(user deleted)
Jul 03, 2004
 i thought that this one was stupid. i didn't know that we could add or multiply the numbers. 
witness
Jul 03, 2004
 This one is annoying...not only because it is hard, but because of all the stupid comments like this one. 
energizer74
Jul 04, 2004
 Penguingirl, it says in the instructions to apply a formula to each number. The formula translated (to anybody who knows even a minute amount of math) would be: (31)^2 (3)^2 (5)^2 (11)^2 (23)^2 (13)^2 to get the answer.
It took me awhile to figure this one out, and it was a great teaser. 
cnmne
Dec 19, 2004
 Sometimes I get lucky. I got this on my second formula (the first was to double each number, which came close). Nonetheless, a clever teaser. 
Confooseled
Oct 05, 2005
 ok yeah that was hard.. im kinda Stupid anyways and i stay confused.. and 3 squared is 9!! im not that dumb like sum people 
Confooseled
Oct 05, 2005
 it was good tho 
schatzy228
Dec 01, 2005
 WONDERFUL 
builder
May 16, 2011
 slick enough for me 
elentir
May 16, 2011
 Too many possible answers to this. I went the 'multiply by zero' route as it is the simplest. I like the 'if n=5, n=n2' formula though. Very creative! 
dsjt
May 16, 2011
 I got two other answers...
I multiply each number by zero to get
0,0,0,0,0,0
Then I divided each number by itself to get
1,1,1,1,1,1 
dsjt
May 16, 2011
 In MOLLYNOODL's defense she was evidently working in base 8.
In that case 3 squared = 10 
auntiesis
May 17, 2011
 Very difficult for me. 
Wimm
Feb 27, 2015
 Many solutions possible, as stated earlier.
Another one: raise each number to power 0.
You get all 1's then, which is a palindrome. 
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