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#Mathematica 30 bytes

Mathematica 30 bytes

#Mathematica 30 bytes

Mathematica 30 bytes

added 123 characters in body
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DavidC
DavidC
  • 25.4k
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  • 52
  • 105

This submission may not qualify, as it makes use of a readily available built-in! But some may find it useful for understanding the connection to Frobenius equations.

The first solution, below, represents 100 pennies; the second solution represents 1 nickel and 95 pennies. And so on...

This submission may not qualify, as it makes use of a readily available built-in! But some may find it useful for understanding the connection to Frobenius equations.

The first solution, below, represents 100 pennies; the second solution represents 1 nickel and 95 pennies. And so on...

Source Link
DavidC
DavidC
  • 25.4k
  • 2
  • 52
  • 105

#Mathematica 30 bytes

The task can be understood as a search for all solutions to the Frobenius equation, 25q+10d+5n+p=t, where q, d, n, p, and t, represent quarters, dimes, nickels, pennies, and total, respectively.

FrobeniusSolve[{25,10,5,1},#]&

The Frobenius equation 25q+10d+5n+p=100 represents all cases that sum to 100 cents.

FrobeniusSolve[{25,10,5,1},100]


{{0, 0, 0, 100}, {0, 0, 1, 95}, {0, 0, 2, 90}, {0, 0, 3, 85}, {0, 0, 4, 80}, {0, 0, 5, 75}, {0, 0, 6, 70}, {0, 0, 7, 65}, {0, 0, 8, 60}, {0, 0, 9, 55}, {0, 0, 10, 50}, {0, 0, 11, 45}, {0, 0, 12, 40}, {0, 0, 13, 35}, {0, 0, 14, 30}, {0, 0, 15, 25}, {0, 0, 16, 20}, {0, 0, 17, 15}, {0, 0, 18, 10}, {0, 0, 19, 5}, {0, 0, 20, 0}, {0, 1, 0, 90}, {0, 1, 1, 85}, {0, 1, 2, 80}, {0, 1, 3, 75}, {0, 1, 4, 70}, {0, 1, 5, 65}, {0, 1, 6, 60}, {0, 1, 7, 55}, {0, 1, 8, 50}, {0, 1, 9, 45}, {0, 1, 10, 40}, {0, 1, 11, 35}, {0, 1, 12, 30}, {0, 1, 13, 25}, {0, 1, 14, 20}, {0, 1, 15, 15}, {0, 1, 16, 10}, {0, 1, 17, 5}, {0, 1, 18, 0}, {0, 2, 0, 80}, {0, 2, 1, 75}, {0,2, 2, 70}, {0, 2, 3, 65}, {0, 2, 4, 60}, {0, 2, 5, 55}, {0, 2, 6, 50}, {0, 2, 7, 45}, {0, 2, 8, 40}, {0, 2, 9, 35}, {0, 2, 10, 30}, {0, 2, 11, 25}, {0, 2, 12, 20}, {0, 2, 13, 15}, {0, 2, 14, 10}, {0, 2, 15, 5}, {0, 2, 16, 0}, {0, 3, 0, 70}, {0, 3, 1, 65}, {0, 3, 2, 60}, {0, 3, 3, 55}, {0, 3, 4, 50}, {0, 3, 5, 45}, {0, 3, 6, 40}, {0, 3, 7, 35}, {0, 3, 8, 30}, {0, 3, 9, 25}, {0, 3, 10, 20}, {0, 3, 11, 15}, {0, 3, 12, 10}, {0, 3, 13, 5}, {0, 3, 14, 0}, {0, 4, 0, 60}, {0, 4, 1, 55}, {0, 4, 2, 50}, {0, 4, 3, 45}, {0, 4, 4, 40}, {0, 4, 5, 35}, {0, 4, 6, 30}, {0, 4, 7, 25}, {0, 4, 8, 20}, {0, 4, 9, 15}, {0, 4, 10, 10}, {0, 4, 11, 5}, {0, 4, 12, 0}, {0, 5, 0, 50}, {0, 5, 1, 45}, {0, 5, 2, 40}, {0, 5, 3, 35}, {0, 5, 4, 30}, {0, 5, 5, 25}, {0, 5, 6, 20}, {0, 5, 7, 15}, {0, 5, 8, 10}, {0, 5, 9, 5}, {0, 5, 10, 0}, {0, 6, 0, 40}, {0, 6, 1, 35}, {0, 6, 2, 30}, {0, 6, 3, 25}, {0, 6, 4, 20}, {0, 6, 5, 15}, {0, 6, 6, 10}, {0, 6, 7, 5}, {0, 6, 8, 0}, {0, 7, 0, 30}, {0, 7, 1, 25}, {0, 7, 2, 20}, {0, 7, 3, 15}, {0, 7, 4, 10}, {0, 7, 5, 5}, {0, 7, 6, 0}, {0, 8, 0, 20}, {0, 8, 1, 15}, {0, 8, 2, 10}, {0, 8, 3, 5}, {0, 8, 4, 0}, {0, 9, 0, 10}, {0, 9, 1, 5}, {0, 9, 2, 0}, {0, 10, 0, 0}, {1, 0, 0, 75}, {1, 0, 1, 70}, {1, 0, 2, 65}, {1, 0, 3, 60}, {1, 0, 4, 55}, {1, 0, 5, 50}, {1, 0, 6, 45}, {1, 0, 7, 40}, {1, 0, 8, 35}, {1, 0, 9, 30}, {1, 0, 10, 25}, {1, 0, 11, 20}, {1, 0, 12, 15}, {1, 0, 13, 10}, {1, 0, 14, 5}, {1, 0, 15, 0}, {1, 1, 0, 65}, {1, 1, 1, 60}, {1, 1, 2, 55}, {1, 1, 3, 50}, {1, 1, 4, 45}, {1, 1, 5, 40}, {1, 1, 6, 35}, {1, 1, 7, 30}, {1, 1, 8, 25}, {1, 1, 9, 20}, {1, 1, 10, 15}, {1, 1, 11, 10}, {1, 1, 12, 5}, {1, 1, 13, 0}, {1, 2, 0, 55}, {1, 2, 1, 50}, {1, 2, 2, 45}, {1, 2, 3, 40}, {1, 2, 4, 35}, {1, 2, 5, 30}, {1, 2, 6, 25}, {1, 2, 7, 20}, {1, 2, 8, 15}, {1, 2, 9, 10}, {1, 2, 10, 5}, {1, 2, 11, 0}, {1, 3, 0, 45}, {1, 3, 1, 40}, {1, 3, 2, 35}, {1, 3, 3, 30}, {1, 3, 4, 25}, {1, 3, 5, 20}, {1, 3, 6, 15}, {1, 3, 7, 10}, {1, 3, 8, 5}, {1, 3, 9, 0}, {1, 4, 0, 35}, {1, 4, 1, 30}, {1, 4, 2, 25}, {1, 4, 3, 20}, {1, 4, 4, 15}, {1, 4, 5, 10}, {1, 4, 6, 5}, {1, 4, 7, 0}, {1, 5, 0, 25}, {1, 5, 1, 20}, {1, 5, 2, 15}, {1, 5, 3, 10}, {1, 5, 4, 5}, {1, 5, 5, 0}, {1, 6, 0, 15}, {1, 6, 1, 10}, {1, 6, 2, 5}, {1, 6, 3, 0}, {1, 7, 0, 5}, {1, 7, 1, 0}, {2, 0, 0, 50}, {2, 0, 1, 45}, {2, 0, 2, 40}, {2, 0, 3, 35}, {2, 0, 4, 30}, {2, 0, 5, 25}, {2, 0, 6, 20}, {2, 0, 7, 15}, {2, 0, 8, 10}, {2, 0, 9, 5}, {2, 0, 10, 0}, {2, 1, 0, 40}, {2, 1, 1, 35}, {2, 1, 2, 30}, {2, 1, 3, 25}, {2, 1, 4, 20}, {2, 1, 5, 15}, {2, 1, 6, 10}, {2, 1, 7, 5}, {2, 1, 8, 0}, {2, 2, 0,  30}, {2, 2, 1, 25}, {2, 2, 2, 20}, {2, 2, 3, 15}, {2, 2, 4, 10}, {2, 2, 5, 5}, {2, 2, 6, 0}, {2, 3, 0, 20}, {2, 3, 1, 15}, {2, 3, 2, 10}, {2, 3, 3, 5}, {2, 3, 4, 0}, {2, 4, 0, 10}, {2, 4, 1, 5}, {2, 4, 2, 0}, {2, 5, 0, 0}, {3, 0, 0, 25}, {3, 0, 1, 20}, {3, 0, 2,  15}, {3, 0, 3, 10}, {3, 0, 4, 5}, {3, 0, 5, 0}, {3, 1, 0, 15}, {3,  1, 1, 10}, {3, 1, 2, 5}, {3, 1, 3, 0}, {3, 2, 0, 5}, {3, 2, 1, 0}, {4, 0, 0, 0}}