SEARCH HOME
 Math Central Quandaries & Queries
 Question from Fiona, a parent: using the numerals 0, 2, 3, 5, 7, 9, make as many six-digit numbers as you can. Rearrange them into ascending order

I can't say I like this problem much.

Firstly it is a little unclear; I assume that you are not allowed to reuse numerals (so 202020 is not a valid answer) but that should be explicit.

Secondly, there are 5*5*4*3*2 = 600 numbers. There is too high a ratio of writing to thinking here.

To do it,

*work through the legal first digits (that is, not 0) in increasing order. Within each of these:
*work through the legal second digits (may be 0, may not equal
first digit) in increasing order. Within each of these:
*work through the legal third digits (may be 0, may not equal
first or second digit) in increasing order. [Etc]

(2)
(20)
(203)
(2035)
203579
203597
(2037)
203759
203795
...
(205)
...
(207)
...
(209)
...
(23)
(230)
...
...
(3)
...

Good Hunting!
RD

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.