Brain Teasers
31, 3, 5, 11, 23, 13
Series
Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.Series
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
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
Actually, 3 squared is not 9!!
Actually, 3 squared is 9
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.
that was a really hard one
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.
Er... multiply each number by 0?
no hcleong, the 2 and 5 would mess that idea up. Although it's interesting that it's nearly a palindrome.
No offense, but I don't think that teaser is that great, but hey, but that's just my oppinion.
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.
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.
Lyceum, the teaser says to apply the same formula to ALL the numbers, not SOME of the numbers.
Great teaser, very clever, very tough.
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.
I guessed it rather quickly, nice one.
LOL AT MOLLYNOODL
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?
Excellent puzzle. Extremely interesting to see the relationships generated between primes, squares and palindromes. A lot of concepts happening here. Thanks!
only a 3.09 difficulty rating ? extremely difficult but very creative
i thought this one was very hard. it was a great idea, though!
Jul 03, 2004
i thought that this one was stupid. i didn't know that we could add or multiply the numbers.
This one is annoying...not only because it is hard, but because of all the stupid comments like this one.
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.
It took me awhile to figure this one out, and it was a great teaser.
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.
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
it was good tho
WONDERFUL
slick enough for me
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=n-2' formula though. Very creative!
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
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
In MOLLYNOODL's defense she was evidently working in base 8.
In that case 3 squared = 10
In that case 3 squared = 10
Very difficult for me.
Many solutions possible, as stated earlier.
Another one: raise each number to power 0.
You get all 1's then, which is a palindrome.
Another one: raise each number to power 0.
You get all 1's then, which is a palindrome.
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