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Palindromic and Tautonymic III (Posted on 2010-03-23) Difficulty: 3 of 5
Make a list of distinct positive integers that are obtained by assigning a different base ten digit from 1 to 9 to each of the capital letters in this expression.

(A+B)*C + (DE)/F + (GH)*I

What are the respective minimum and maximum positive palindromes from amongst the elements that correspond to the foregoing list?

As a bonus, what are the respective minimum and maximum positive tautonymic numbers that are included in the list? How about the respective maximum and minimum prime numbers?

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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palindrome min/max | Comment 9 of 11 |

On my earlier posting I had assumed that each of the three triplets had to be positive, but clearly only the entire expression must be positive.  I found 3624 combinations which yielded palindromes, but this did not exclude the duplication of interchanging A and B values which led to the same totals.

The lowest palindrome I found was 33.  For example, this was found when assigning 4 5 3  2 8 6  1 9 7  to the letters.  There were a total of 36 assignments yielding 33 (counting each of the a-b b-a cases).

The highest I found was 327680.  I found only one case (or two by swap of a-b) for this  6 7 3  9 1 2  4 8 5, which was really an outlier, since the next highest value was only 131131.

Probably these results have already been posted, so I'll read them.  Perhaps K.S. will want to invent a "cataclysmic number" for the next puzzle.

 e  a,br  yielding this valuedmany weretar


  Posted by ed bottemiller on 2010-03-23 21:12:47
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