Functions
and subroutines used in the Puzzlets are discussed here, with
explanations of how they work and why they were designed this way.Just what is the difference between a function and a subroutine? A subroutine is a separate piece of code you can call to do a job and then carry on where you left off. A function is a subroutine, but has the additional feature that it can return a value to the routine that called it. So a function designed, say, to find the average of three integers, might be called like this: ave = Average(a, b, c) The name of the function is Average(). The parameters passed to the function are a, b, and c. The function returns a value, which in this case is (a + b + c)/3, and the result is stored in variable ave. Finally, note that what you pass to a function or subroutine are called parameters. What a function or subroutine receives from the calling routine are known as arguments - the same as parameters, but known differently by sender and receiver. Note: some of these functions have been improved and otherwise matured since the earlier Puzzlets were published. If you want more information on an older version, please follow the e-mail link below. Click on an item to view it (they're listed alphabetically): |

Title | Description |

AllCharsDiff() |
Checks
every character of the argument to see if they're all different to each
other. |

AllDiffBy2() |
Checks
every digit of the argument differs from its
neighbours by exactly 2, such as 31357, etc. |

AllDigitsDifferent() |
Checks
that each digit of the argument is unique, such as 31254, 97561,
etc. No longer recommended: use AddCharsDiff() instead (it's
faster). |

AllDigitsEven() |
Checks that each digit of the argument is even, such as 22482, 6824, etc. |

AllDigitsOdd() |
Checks that each digit of the argument is odd, such as 11371, 5937, etc. |

AllDigitsSame() |
Checks
that each digit of the argument is unique, such as 222, 5555555, etc. |

Anagrams() |
Checks
that one the arguments is an anagram of the other. Fast, but only
works for integer arguments. For other character mixes, see
function IsAnagram(). |

Bin2Dec() |
Converts the argument from a binary number in string format to a denary integer. |

ChangeBase() |
Converts
the first argument from a denary integer to the number base indicated
by the second argument, with the output in string format. |

Cont_Dig_Sum() |
Obtains the argument's CDS (Contiguous
Digit Sum, the sum of all the smaller
integers that can be formed from it, using only contiguous digits). For example, CDS(8358) is 1393, the sum of 8,83,835,3,35,358,5,58,8. |

CountPrimeFactors() | Counts the prime factors of its argument and returns the number of factors (not the factors themselves) to the calling routine. |

Dec2Bin() |
Converts
the argument from a denary integer to a binary number in string format. |

Dec2Oct() |
Converts the argument from a denary integer to an octal number in string format. |

Factorial() |
Returns
the factorial of its argument. Thus argument 6 returns 6! = 720. |

FinalDigitProduct() |
Finds the single digit resulting from repeated multiplying of its arugment's digits together. |

GetNextPrime() |
Finds the prime number whose value is closest to (but greater than) its argument and returns it to the calling routine. |

Hex2Dec() |
Converts a hexadecimal argument to denary format and returns it to the calling routine. |

Is9Pandigital() |
Checks
that argument uses every digit 1 to 9 inclusive once and once only. |

Is10Pandigital() |
Checks that argument uses every digit 0 to 9 inclusive once and once only. |

IsAbundant() |
Checks
that argument is an Abundant Number. |

IsAchillesNr() | Checks that the argument is an Achilles number, that is, it's not a square and each of its prime factors occur at least twice. |

IsAnagram() | Checks that one argument is an anagram of the other. Works for any kind of characters. |

IsAPower() | Checks that the argument is a power of some smaller digit. Returns the root or, if it's not a power, 0. |

IsASquare() |
Checks
that argument is a perfect square, such as 625, 1000, etc. |

IsDigNum() |
Checks
that argument can be divided by both product and sum of its own
digits, such as 36, 8112, etc. |

IsDownOrdered() |
Checks
that argument's digits are arranged in descending order, such as 9862,
87551, etc. |

IsForwardRun() |
Checks
that argument's digits are arranged in consecutive, ascending order,
such as 234, 12, 45678, etc. |

IsOddAbundant() |
Checks
that the argument is an odd Abundant Number. |

IsPalidrome() |
Checks
that argument's digits are palindromic, such as 232, 9445449, 1551, etc. |

IsPrime() |
Checks
that argument is a prime number (that is, divisible only by itself and
1), such as 7, 71, etc. |

IsReverseRun() |
Checks that argument's digits are arranged in consecutive, descending order, such as 432, 21, 87654, etc. |

IsUpOrdered() |
Checks that argument's digits are arranged in ascending order, such as 2689, 23669, etc. |

MaxInt() | Returns the greatest-value digit of the argument. |

MinInt() | Returns the least-value digit of the argument. |

NoDigitsIncluded() |
Checks that none of the digits in its
first argument are included in its second argument. |

NoZeroes() |
Checks
that none of argument's digits are equal to zero, such as 24413, 98,
etc. |

PrintPrimeFactors() |
Prints
out the prime factors of its argument in ascending order. |

PrimeFactorSum() |
Returns
the sum of the prime factors of its argument. |

ProdNumericStrings() |
Pass two integers in string
format to this function and it will return the product of the two
integers in string format , up to 256 digits in length. |

ProductDigits() |
Returns
the product of argument's digits. Thus, 24 returns 8, 5127 returns 70,
etc. |

RemoveTrailingZeroes() |
Returns
the argument with any trailing zeroes removed. Thus, "356700" is
returned as "3567" etc. |

Reverse() |
Returns
the reverse of its argument. So 98761 returns 16789, 25 returns 52, etc. |

ReverseString() |
Returns the reverse of its argument. So "25" returns "52", "abc" returns "cba", etc. |

SumDigits() |
Returns the sum of argument's digits. Thus, 24 returns 6, 7189 returns 25, etc. |

SumFactorials() |
Returns the sum of the factorials of
the digits of its argument. 253 returns 2! + 5! + 3! = 128. |

SumPowers() |
Returns
sum of powers of arguments digits in position order, so 543 returns 5^1
+ 4^2 + 3^3 = 48, and so on. |

SumSquares() |
Returns the sum of the squares of
the digits of its argument. 253 returns 2^{2} + 5^{2} + 3^{2} = 38. |

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Last Updated: September 19th, 2010.