RosettaCodeData/Task/Colorful-numbers/00-TASK.txt

A '''colorful number''' is a non-negative base 10 integer where the product of every sub group of consecutive digits is unique.


;E.G.

24753 is a colorful number. 2, 4, 7, 5, 3, (2×4)8, (4×7)28, (7×5)35, (5×3)15, (2×4×7)56, (4×7×5)140, (7×5×3)105, (2×4×7×5)280, (4×7×5×3)420, (2×4×7×5×3)840

Every product is unique.


2346 is '''not''' a colorful number. 2, 3, 4, '''6''', (2×3)'''6''', (3×4)12, (4×6)'''24''', (2×3×4)'''24''', (3×4×6)72, (2×3×4×6)144

The products '''6''' and '''24''' are repeated.


Single digit numbers '''are''' considered to be colorful. A colorful number larger than 9 cannot contain a repeated digit, the digit 0 or the digit 1. As a consequence, there is a firm upper limit for colorful numbers; no colorful number can have more than 8 digits.


;Task

* Write a routine (subroutine, function, procedure, whatever it may be called in your language) to test if a number is a colorful number or not.
* Use that routine to find all of the colorful numbers less than 100.
* Use that routine to find the largest possible colorful number.


;Stretch

* Find and display the count of colorful numbers in each order of magnitude.
* Find and show the total count of '''all''' colorful numbers.


''Colorful numbers have no real number theory application. They are more a recreational math puzzle than a useful tool.''