# Numbers that represent four tuples

Is it possible to make up a distinct number that is made up of four tuples. One of which indicates the direction of the arrangement of the other three.

Say, $9*4*7 = 252 \ . \ 252$ is distinct in the sense that you cannot get it as a multiplication of 3 distinct single digit numbers other than 9, 4, 7. Now, the problem is 252 could mean, any of the three orders. Say, 947, 497, 974. Is there any way to add a sense of direction/arrangement to it?

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Your question is unclear. What do you mean by "made up of four tuples"? In fact, what do you mean by "tuples"? –  yrudoy Oct 5 '10 at 12:46

Yes. Try creating your number like this:

Suppose your 3-tuple has values (a,b,c). Then generate your distinct number as follows:

2^a * 3^b * 5^c

Since these are prime bases, this number will be unique for any 3 values and will be recoverable, in that you can factor your number and get back all 3 numbers and their orders. To extend this to any n-tuple just use more prime number bases.

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