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Pandigital Ponder II (Posted on 2014-08-19) Difficulty: 3 of 5
Each of P, Q, R and S together uses the base ten digits from 1 to 9 exactly once.

What are the respective minimum and maximum value of P*Q*R*S?

No Solution Yet Submitted by K Sengupta    
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Guessing at the maximum (spoiler?) | Comment 2 of 3 |
Here, I think that we want the numbers to be close together.  So we have a 3 digit number and three 2 digit numbers.

I guess that the three digit number starts with a 9 and the others start with 8, 7, 6.  I guess that they are followed by 5, 4, 3 and 2, in reverse order.

First intuition, therefore, is 921*83*74*65 = 367,690,830.

I am less confident about this guess.  It is based on the well-known result that if two numbers have a constant sum, then their product is increased if they are closer together.

So, for instance, 74*65 < 76*64.  Which is why I assigned the digits 5,4,3 and 2 in reverse order.

Gotta go.



  Posted by Steve Herman on 2014-08-19 17:50:24
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