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Category: | Series |

Submitted By: | im_para_noid |

Fun: | (2.78) |

Difficulty: | (3.04) |

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

Show Answer |

Posted by mollynoodl | 07/25/02 |

Actually, 3 squared is not 9!! | |

Posted by SkEwL_gUrl | 07/26/02 |

Actually, 3 squared is 9 | |

Posted by george1978 | 07/29/02 |

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. | |

Posted by Stargirl | 07/29/02 |

that was a really hard one | |

Posted by sillywilly | 07/31/02 |

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. | |

Posted by dsquared | 08/15/02 |

Great teaser, very clever, very tough. | |

Posted by mpeoples | 08/15/02 |

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. | |

Posted by majd | 08/18/02 |

I guessed it rather quickly, nice one. | |

Posted by klopper | 09/09/02 |

LOL AT MOLLYNOODL | |

Posted by dsquared | 09/10/02 |

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? | |

Posted by jimbo | 10/29/03 |

Excellent puzzle. Extremely interesting to see the relationships generated between primes, squares and palindromes. A lot of concepts happening here. Thanks! :D | |

Posted by griphook | 10/29/03 |

only a 3.09 difficulty rating ? extremely difficult but very creative | |

Posted by witness | 07/03/04 |

This one is annoying...not only because it is hard, but because of all the stupid comments like this one. :lol: | |

Posted by cnmne | 12/19/04 |

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. | |

Posted by Confooseled | 10/05/05 |

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 | |

Posted by Confooseled | 10/05/05 |

it was good tho | |

Posted by schatzy228 | 12/01/05 |

WONDERFUL 8) | |

Posted by builder | 05/16/11 |

slick enough for me | |

Posted by elentir | 05/16/11 |

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! :D | |

Posted by dsjt | 05/16/11 |

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 | |

Posted by dsjt | 05/16/11 |

In MOLLYNOODL's defense she was evidently working in base 8. In that case 3 squared = 10 | |

Posted by auntiesis | 05/17/11 |

Very difficult for me. :-? :roll: | |

Posted by Wimm | 02/27/15 |

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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