40 41 42 43

40.py

@@ -0,0 +1,28 @@
+#-*- coding:utf-8 -*-
+
+"""
+An irrational decimal fraction is created by concatenating the positive integers:
+
+0.123456789101112131415161718192021...
+
+It can be seen that the 12th digit of the fractional part is 1.
+
+If dn represents the nth digit of the fractional part, find the value of the following expression.
+
+d1 × d10 × d100 × d1000 × d10000 × d100000 × d1000000
+"""
+
+def digit_at(n):
+    digits = 1
+    n = n - 1
+    while True:
+        numbers = 9 * pow(10, digits-1) * digits
+        if n > numbers:
+            n = n - numbers
+        else:
+            break
+        digits = digits + 1
+    num = n / digits + pow(10, digits-1)
+    return int(str(num)[n % digits])
+
+print digit_at(1) * digit_at(10) * digit_at(100) * digit_at(1000) * digit_at(10000) * digit_at(100000) * digit_at(1000000)

41.py

@@ -0,0 +1,19 @@
+#-*- coding:utf-8 -*-
+
+"""
+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, 2143 is a 4-digit pandigital and is also prime.
+
+What is the largest n-digit pandigital prime that exists?
+"""
+
+
+import prime
+from itertools import permutations
+
+for i in permutations(range(7, 0, -1)):
+    num = 0
+    for n in i:
+        num = num * 10 + n
+    if prime.isprime(num):
+        print num
+        break

42.py

@@ -0,0 +1,39 @@
+#-*- coding:utf-8 -*-
+
+"""
+The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:
+
+1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+
+By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.
+
+Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?
+"""
+
+import math
+
+
+def is_triangle(n):
+    for i in xrange(1, int(math.sqrt(2*n))+1):
+        if i*(i+1) == n*2:
+            return True
+    return False
+
+
+def main():
+    num = 0
+    fp = open('words.txt', 'r')
+    words_string = fp.read()
+    words_list = map(lambda x: x.strip('"'), words_string.split(','))
+    for word in words_list:
+        total = 0
+        for w in word:
+            total += ord(w) - ord('A') + 1
+        if is_triangle(total):
+            num += 1
+    print num      
+    fp.close()
+
+
+if __name__ == '__main__':
+    main()

43.py

@@ -0,0 +1,46 @@
+#-*- coding:utf-8 -*-
+
+"""
+The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.
+
+Let d1 be the 1st digit, d2 be the 2nd digit, and so on. In this way, we note the following:
+
+d2d3d4=406 is divisible by 2
+d3d4d5=063 is divisible by 3
+d4d5d6=635 is divisible by 5
+d5d6d7=357 is divisible by 7
+d6d7d8=572 is divisible by 11
+d7d8d9=728 is divisible by 13
+d8d9d10=289 is divisible by 17
+Find the sum of all 0 to 9 pandigital numbers with this property.
+"""
+
+from itertools import permutations
+
+def num(n):
+    s = 0
+    for i in n:
+        s = s*10 + i
+    return s
+
+
+def subdiv(l, n):
+    return num(l) % n == 0
+
+
+def main():
+    total = 0
+    for p in permutations(range(0, 10)):
+        if subdiv(p[7:10], 17) and \
+           subdiv(p[6:9], 13) and \
+           subdiv(p[5:8], 11) and \
+           subdiv(p[4:7], 7) and \
+           subdiv(p[3:6], 5) and \
+           subdiv(p[2:5], 3) and \
+           subdiv(p[1:4], 2) :
+            total += num(p)
+    print total
+
+
+if __name__ == '__main__':
+    main()

words.txt

@@ -0,0 +1 @@
+"A","ABILITY","ABLE","ABOUT","ABOVE","ABSENCE","ABSOLUTELY","ACADEMIC","ACCEPT","ACCESS","ACCIDENT","ACCOMPANY","ACCORDING","ACCOUNT","ACHIEVE","ACHIEVEMENT","ACID","ACQUIRE","ACROSS","ACT","ACTION","ACTIVE","ACTIVITY","ACTUAL","ACTUALLY","ADD","ADDITION","ADDITIONAL","ADDRESS","ADMINISTRATION","ADMIT","ADOPT","ADULT","ADVANCE","ADVANTAGE","ADVICE","ADVISE","AFFAIR","AFFECT","AFFORD","AFRAID","AFTER","AFTERNOON","AFTERWARDS","AGAIN","AGAINST","AGE","AGENCY","AGENT","AGO","AGREE","AGREEMENT","AHEAD","AID","AIM","AIR","AIRCRAFT","ALL","ALLOW","ALMOST","ALONE","ALONG","ALREADY","ALRIGHT","ALSO","ALTERNATIVE","ALTHOUGH","ALWAYS","AMONG","AMONGST","AMOUNT","AN","ANALYSIS","ANCIENT","AND","ANIMAL","ANNOUNCE","ANNUAL","ANOTHER","ANSWER","ANY","ANYBODY","ANYONE","ANYTHING","ANYWAY","APART","APPARENT","APPARENTLY","APPEAL","APPEAR","APPEARANCE","APPLICATION","APPLY","APPOINT","APPOINTMENT","APPROACH","APPROPRIATE","APPROVE","AREA","ARGUE","ARGUMENT","ARISE","ARM","ARMY","AROUND","ARRANGE","ARRANGEMENT","ARRIVE","ART","ARTICLE","ARTIST","AS","ASK","ASPECT","ASSEMBLY","ASSESS","ASSESSMENT","ASSET","ASSOCIATE","ASSOCIATION","ASSUME","ASSUMPTION","AT","ATMOSPHERE","ATTACH","ATTACK","ATTEMPT","ATTEND","ATTENTION","ATTITUDE","ATTRACT","ATTRACTIVE","AUDIENCE","AUTHOR","AUTHORITY","AVAILABLE","AVERAGE","AVOID","AWARD","AWARE","AWAY","AYE","BABY","BACK","BACKGROUND","BAD","BAG","BALANCE","BALL","BAND","BANK","BAR","BASE","BASIC","BASIS","BATTLE","BE","BEAR","BEAT","BEAUTIFUL","BECAUSE","BECOME","BED","BEDROOM","BEFORE","BEGIN","BEGINNING","BEHAVIOUR","BEHIND","BELIEF","BELIEVE","BELONG","BELOW","BENEATH","BENEFIT","BESIDE","BEST","BETTER","BETWEEN","BEYOND","BIG","BILL","BIND","BIRD","BIRTH","BIT","BLACK","BLOCK","BLOOD","BLOODY","BLOW","BLUE","BOARD","BOAT","BODY","BONE","BOOK","BORDER","BOTH","BOTTLE","BOTTOM","BOX","BOY","BRAIN","BRANCH","BREAK","BREATH","BRIDGE","BRIEF","BRIGHT","BRING","BROAD","BROTHER","BUDGET","BUILD","BUILDING","BURN","BUS","BUSINESS","BUSY","BUT","BUY","BY","CABINET","CALL","CAMPAIGN","CAN","CANDIDATE","CAPABLE","CAPACITY","CAPITAL","CAR","CARD","CARE","CAREER","CAREFUL","CAREFULLY","CARRY","CASE","CASH","CAT","CATCH","CATEGORY","CAUSE","CELL","CENTRAL","CENTRE","CENTURY","CERTAIN","CERTAINLY","CHAIN","CHAIR","CHAIRMAN","CHALLENGE","CHANCE","CHANGE","CHANNEL","CHAPTER","CHARACTER","CHARACTERISTIC","CHARGE","CHEAP","CHECK","CHEMICAL","CHIEF","CHILD","CHOICE","CHOOSE","CHURCH","CIRCLE","CIRCUMSTANCE","CITIZEN","CITY","CIVIL","CLAIM","CLASS","CLEAN","CLEAR","CLEARLY","CLIENT","CLIMB","CLOSE","CLOSELY","CLOTHES","CLUB","COAL","CODE","COFFEE","COLD","COLLEAGUE","COLLECT","COLLECTION","COLLEGE","COLOUR","COMBINATION","COMBINE","COME","COMMENT","COMMERCIAL","COMMISSION","COMMIT","COMMITMENT","COMMITTEE","COMMON","COMMUNICATION","COMMUNITY","COMPANY","COMPARE","COMPARISON","COMPETITION","COMPLETE","COMPLETELY","COMPLEX","COMPONENT","COMPUTER","CONCENTRATE","CONCENTRATION","CONCEPT","CONCERN","CONCERNED","CONCLUDE","CONCLUSION","CONDITION","CONDUCT","CONFERENCE","CONFIDENCE","CONFIRM","CONFLICT","CONGRESS","CONNECT","CONNECTION","CONSEQUENCE","CONSERVATIVE","CONSIDER","CONSIDERABLE","CONSIDERATION","CONSIST","CONSTANT","CONSTRUCTION","CONSUMER","CONTACT","CONTAIN","CONTENT","CONTEXT","CONTINUE","CONTRACT","CONTRAST","CONTRIBUTE","CONTRIBUTION","CONTROL","CONVENTION","CONVERSATION","COPY","CORNER","CORPORATE","CORRECT","COS","COST","COULD","COUNCIL","COUNT","COUNTRY","COUNTY","COUPLE","COURSE","COURT","COVER","CREATE","CREATION","CREDIT","CRIME","CRIMINAL","CRISIS","CRITERION","CRITICAL","CRITICISM","CROSS","CROWD","CRY","CULTURAL","CULTURE","CUP","CURRENT","CURRENTLY","CURRICULUM","CUSTOMER","CUT","DAMAGE","DANGER","DANGEROUS","DARK","DATA","DATE","DAUGHTER","DAY","DEAD","DEAL","DEATH","DEBATE","DEBT","DECADE","DECIDE","DECISION","DECLARE","DEEP","DEFENCE","DEFENDANT","DEFINE","DEFINITION","DEGREE","DELIVER","DEMAND","DEMOCRATIC","DEMONSTRATE","DENY","DEPARTMENT","DEPEND","DEPUTY","DERIVE","DESCRIBE","DESCRIPTION","DESIGN","DESIRE","DESK","DESPITE","DESTROY","DETAIL","DETAILED","DETERMINE","DEVELOP","DEVELOPMENT","DEVICE","DIE","DIFFERENCE","DIFFERENT","DIFFICULT","DIFFICULTY","DINNER","DIRECT","DIRECTION","DIRECTLY","DIRECTOR","DISAPPEAR","DISCIPLINE","DISCOVER","DISCUSS","DISCUSSION","DISEASE","DISPLAY","DISTANCE","DISTINCTION","DISTRIBUTION","DISTRICT","DIVIDE","DIVISION","DO","DOCTOR","DOCUMENT","DOG","DOMESTIC","DOOR","DOUBLE","DOUBT","DOWN","DRAW","DRAWING","DREAM","DRESS","DRINK","DRIVE","DRIVER","DROP","DRUG","DRY","DUE","DURING","DUTY","EACH","EAR","EARLY","EARN","EARTH","EASILY","EAST","EASY","EAT","ECONOMIC","ECONOMY","EDGE","EDITOR","EDUCATION","EDUCATIONAL","EFFECT","EFFECTIVE","EFFECTIVELY","EFFORT","EGG","EITHER","ELDERLY","ELECTION","ELEMENT","ELSE","ELSEWHERE","EMERGE","EMPHASIS","EMPLOY","EMPLOYEE","EMPLOYER","EMPLOYMENT","EMPTY","ENABLE","ENCOURAGE","END","ENEMY","ENERGY","ENGINE","ENGINEERING","ENJOY","ENOUGH","ENSURE","ENTER","ENTERPRISE","ENTIRE","ENTIRELY","ENTITLE","ENTRY","ENVIRONME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E","TRADITION","TRADITIONAL","TRAFFIC","TRAIN","TRAINING","TRANSFER","TRANSPORT","TRAVEL","TREAT","TREATMENT","TREATY","TREE","TREND","TRIAL","TRIP","TROOP","TROUBLE","TRUE","TRUST","TRUTH","TRY","TURN","TWICE","TYPE","TYPICAL","UNABLE","UNDER","UNDERSTAND","UNDERSTANDING","UNDERTAKE","UNEMPLOYMENT","UNFORTUNATELY","UNION","UNIT","UNITED","UNIVERSITY","UNLESS","UNLIKELY","UNTIL","UP","UPON","UPPER","URBAN","US","USE","USED","USEFUL","USER","USUAL","USUALLY","VALUE","VARIATION","VARIETY","VARIOUS","VARY","VAST","VEHICLE","VERSION","VERY","VIA","VICTIM","VICTORY","VIDEO","VIEW","VILLAGE","VIOLENCE","VISION","VISIT","VISITOR","VITAL","VOICE","VOLUME","VOTE","WAGE","WAIT","WALK","WALL","WANT","WAR","WARM","WARN","WASH","WATCH","WATER","WAVE","WAY","WE","WEAK","WEAPON","WEAR","WEATHER","WEEK","WEEKEND","WEIGHT","WELCOME","WELFARE","WELL","WEST","WESTERN","WHAT","WHATEVER","WHEN","WHERE","WHEREAS","WHETHER","WHICH","WHILE","WHILST","WHITE","WHO","WHOLE","WHOM","WHOSE","WHY","WIDE","WIDELY","WIFE","WILD","WILL","WIN","WIND","WINDOW","WINE","WING","WINNER","WINTER","WISH","WITH","WITHDRAW","WITHIN","WITHOUT","WOMAN","WONDER","WONDERFUL","WOOD","WORD","WORK","WORKER","WORKING","WORKS","WORLD","WORRY","WORTH","WOULD","WRITE","WRITER","WRITING","WRONG","YARD","YEAH","YEAR","YES","YESTERDAY","YET","YOU","YOUNG","YOUR","YOURSELF","YOUTH"