' Puzzlet #224.
' ProSum Numbers are obtained when the product
' of an integer's digits divided by the sum of
' its digits is itself an integer.  If the
' resultant integer can be used to produce yet
' another integer in the same way, a sequence
' is formed. It is terminated when a new term
' is less than 10.
' The first term must be at least 10, or an
' endless loop is formed. 
' Find the lowest starting term for a sequence
' of two ProSum Numbers, then do the same for
' three terms and four terms.
' By Dave Ellis.

' Declarations
declare ProductDigits(p: int)
declare SumDigits(s: int)
declare PrintResult()
def count, flag, n, prod, sum, target, term: int
def quotient: double

' Screen Setup
color 11, 0: cls
openconsole
print "1st Term   Nr Of Terms   Last Term"
color 14, 0
print

' Initialisations
n = 10
target = 0

' Main routine
do	
	term = n: 'save n
	count = 0: 'initialise count
	flag = -1: 'set flag to TRUE
	do
		prod = ProductDigits(term): 'get product
		sum = Sumdigits(term): 'get sum
		quotient = prod/sum: 'calculate quotient
		if quotient = int(quotient): 'is it an integer?
			count = count + 1: 'yes - increment tally
			term = quotient: 'yes - get next term
		else: 'no
			flag = 0: 'set flag to FALSE
		endif
	until (flag = 0) | (term < 10)
	if count > target: 'target reached?
		PrintResult(): 'yes - print result
		target = target + 1: 'yes - get next target
	endif
	n = n + 1: 'increment sequence start
until target = 3

' finished
color 11, 0
print: print "That's all, Folks!"
print: print "Press any key to exit ... ",
do: until inkey$ <> ""
closeconsole
end

' +++ Functions and Subroutines +++

sub ProductDigits(p)
' Returns the product of the 
' digits of integer p. Will
' give incorrect answer if p
' larger than defined limits
' for integers.
' By Dave Ellis.
def tot: int
tot = 1
do
	' separate out LSD and totalise
	tot = tot * (p % 10)
	' chop off LSD
	p = p/10
until p = 0: ' all chopped off!
return tot

sub SumDigits(s)
' Returns the sum of the 
' digits of integer s. Will
' give incorrect answer if s
' larger than defined limits
' for integers.
' By Dave Ellis.
def tot: int
tot = 0
do
	' separate out LSD and totalise
	tot = tot + (s % 10)
	' chop off LSD
	s = s/10
until s = 0: 'all chopped off!
return tot

sub PrintResult()
print using ("#######", n),
print using ("##########", count + 1),
print using ("#############", term)
return