34 lines
1.3 KiB
Plaintext
34 lines
1.3 KiB
Plaintext
A '''colorful number''' is a non-negative base 10 integer where the product of every sub group of consecutive digits is unique.
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;E.G.
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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
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Every product is unique.
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2346 is '''not''' a colorful number. 2, 3, 4, '''6''', (2×3)'''6''', (3×4)12, (4×6)24, (2×3×4)48, (3×4×6)72, (2×3×4×6)144
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The product '''6''' is repeated.
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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.
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;Task
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* 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.
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* Use that routine to find all of the colorful numbers less than 100.
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* Use that routine to find the largest possible colorful number.
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;Stretch
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* Find and display the count of colorful numbers in each order of magnitude.
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* Find and show the total count of '''all''' colorful numbers.
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''Colorful numbers have no real number theory application. They are more a recreational math puzzle than a useful tool.''
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