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src/further_examples/project_euler/digit_canceling.py~

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+#!/usr/bin/python3
+# mari von steinkirch @2013
+# steinkirch at gmail
+
+'''
+The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.
+
+We shall consider fractions like, 30/50 = 3/5, to be trivial examples.
+
+There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator.
+
+If the product of these four fractions is given in its lowest common terms, find the value of the denominator.
+'''
+
+def find_sum_proper_divisors(n):
+    sum_proper_div = 0
+    for i in range(1, n):
+        if n%i == 0:
+            sum_proper_div += i
+    return sum_proper_div
+
+
+def amicable_numbers(N):
+    sum_div_list = [find_sum_proper_divisors(i) for i in range(1, N+1)]
+    sum_amicable_numbers = 0
+    set_div = set()    
+    for a in range(1, N):
+        da = sum_div_list[a-1]
+        if da < N:
+            b = da
+            db = sum_div_list[b-1]
+            if a != b and db == a and a not in set_div and b not in set_div:
+                sum_amicable_numbers += a + b
+                set_div.add(a)
+                set_div.add(b)
+    return sum_amicable_numbers
+    
+
+def main():
+    print(amicable_numbers(10000))
+    print('Tests Passed!')
+                   
+if __name__ == '__main__':
+    main()
+

src/further_examples/project_euler/pandigital_prod.py

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+#!/usr/bin/python3
+# mari von steinkirch @2013
+# steinkirch at gmail
+
+
+# very dumb version, need to be optimized 
+
+'''
+We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.
+
+The product 7254 is unusual, as the identity, 39 x186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.
+
+Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.
+
+HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
+'''
+
+def is_pandigital(n):
+    size = len(n)
+    pan = set([x for x in range(1,size + 1)])
+    for i in n:
+        if int(i) in pan:
+            pan = pan - {int(i)}
+        else:
+            return False
+    return True
+    
+def find_multiples(n):
+    multiples = set([1, n])
+    for i in range(2, n):
+        if n%i == 0:
+            multiples.add(i)
+            multiples.add(n//i)       
+    return multiples
+ 
+
+def find_pandigital():
+    sum_pan = 0
+  
+    for i in range(10, 987654322):
+        if i//10 == 0:
+            continue
+        digits = set(str(i))
+        if len(digits) != len(str(i)):
+            continue
+        multiples = find_multiples(i)
+        mult_set = set()
+        for j in multiples:
+            for c in str(j):
+                if c in digits or int(c) == 0:
+                    continue
+            for c in str(j):
+                mult_set.add(c)            
+            k = i//j
+            for c in str(k):
+                if c in digits or int(c) == 0:
+                    continue
+            for c in str(k):
+                mult_set.add(c)  
+            if len(mult_set ) == 9:
+                sum_pan += j + k + i               
+    return sum_pan
+        
+    
+   
+def main():
+    assert(is_pandigital('15234') == True )
+    assert(is_pandigital('15233') == False ) 
+    
+    print(find_pandigital()) 
+    
+    print('Tests Passed!')
+                   
+if __name__ == '__main__':
+    main()
+

src/further_examples/project_euler/pandigital_prod.py~

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+#!/usr/bin/python3
+# mari von steinkirch @2013
+# steinkirch at gmail
+
+'''
+We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.
+
+The product 7254 is unusual, as the identity, 39 x186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.
+
+Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.
+
+HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.
+'''
+
+def is_pandigital(n):
+    size = len(n)
+    pan = set([x for x in range(1,size + 1)])
+    for i in n:
+        if int(i) in pan:
+            pan = pan - {int(i)}
+        else:
+            return False
+    return True
+    
+def find_multiples(n):
+    multiples = set([1, n])
+    for i in range(2, n):
+        if n%i == 0:
+            multiples.add(i)
+            multiples.add(n//i)       
+    return multiples
+ 
+
+def find_pandigital():
+    sum_pan = 0
+  
+    for i in range(10, 987654322):
+        if i//10 == 0:
+            continue
+        digits = set(str(i))
+        if len(digits) != len(str(i)):
+            continue
+        multiples = find_multiples(i)
+        mult_set = set()
+        for j in multiples:
+            for c in str(j):
+                if c in digits or int(c) == 0:
+                    continue
+            for c in str(j):
+                mult_set.add(c)            
+            k = i//j
+            for c in str(k):
+                if c in digits or int(c) == 0:
+                    continue
+            for c in str(k):
+                mult_set.add(c)  
+            if len(mult_set ) == 9:
+                sum_pan += j + k + i               
+    return sum_pan
+        
+    
+   
+def main():
+    assert(is_pandigital('15234') == True )
+    assert(is_pandigital('15233') == False ) 
+    
+    print(find_pandigital()) 
+    
+    print('Tests Passed!')
+                   
+if __name__ == '__main__':
+    main()
+