├── 79_Passcode_Derivation.py ├── P206_conclealed_square.py ├── P21_Amicable_numbers.py ├── P23_Name_scores.py ├── P25_Hundred_Digit_fibo.py ├── P26_Reciprocal_cycles.py ├── P27_Quadratic_Primes.py ├── P28_Number_Spiral_Diagonals.py ├── P30_Digit_fifth_Powers.py ├── P31_Coin_Sums.py ├── P32_Pandigital_Products.py ├── P33_Digit_Cancel.py ├── P34_Digit_Factorials.py ├── P357_Prime_Generating_int.py ├── P35_Circular_Primes.py ├── P36_Double_Palindrome.py ├── P37_Truncatable _Primes.py ├── P387_Harshad_Numbers.py ├── P38_Pandigital_Multiples.py ├── P39_Integer_Triangles.py ├── P40_Champernoven's_Constant.py ├── P41_Pandigital_Prime.py ├── P42_coded_triangle.py ├── P43_Substring_Divisibility.py ├── P44_Pentagon_Numbers.py ├── P45_Triangular_Pent_Hex.py ├── P46_Goldbach's_Conjecture.py ├── P47_Distinct_Prime_factors.py ├── P48_self_Powers.py ├── P49_Prime_Permutations.py ├── P50_consecutive_Prime_sum.py ├── P52_Permuted_Multiples.py ├── P53_Combinatorial_Selection.py ├── P55_Lychreal_Numbers.py ├── P56_Power_sums.py ├── P57_Square_Root_Convergents.py ├── P58_Spiral_Primes.py ├── P59_XOR_Decryption.py ├── P63_Powerful_Digit_Counts.py ├── P69_TotientMax.py ├── P71_Ordered_Fractions.py ├── P76_Counting_Summations.py ├── P81_Pathsum_2ways.py ├── P92_Square_Digit_Chains.py ├── P97_Large non-Mersenne prime.py ├── P99_Largest_Exp.py └── README.md /79_Passcode_Derivation.py: -------------------------------------------------------------------------------- 1 | pre=[set() for i in range(10)] 2 | pos=[set() for i in range(10)] 3 | for i in range(50): 4 | n=input(); 5 | a=int(n[0]) 6 | b=int(n[1]) 7 | c=int(n[2]) 8 | pos[a].add(b); 9 | pos[a].add(c); 10 | pos[b].add(c) 11 | pre[b].add(a); 12 | pre[c].add(b) 13 | pre[c].add(a) 14 | for i in range (10): 15 | print(pre[i],i,pos[i],sep=' ') 16 | -------------------------------------------------------------------------------- /P206_conclealed_square.py: -------------------------------------------------------------------------------- 1 | import math 2 | def chk(x): 3 | th="1234567890"; 4 | n=str(x*x); 5 | # print(n) 6 | f=0; 7 | for j in range (10): 8 | #print (th[j],n[j*2+1]) 9 | if(th[j]!=n[j*2]): 10 | f=1; 11 | break; 12 | return f; 13 | for i in range(int(math.sqrt(10203040506070809)),10000000000000): 14 | if(chk(i*10)==0): 15 | print(i) 16 | break 17 | -------------------------------------------------------------------------------- /P21_Amicable_numbers.py: -------------------------------------------------------------------------------- 1 | # cook your dish here 2 | # your code goes here 3 | import math 4 | ct=0; 5 | lol=[0]*100001 6 | for i in range (2,10001): 7 | x=1; 8 | y=int(math.sqrt(i)); 9 | for j in range (2,y+1): 10 | if(i%j==0): 11 | x=x+j; 12 | if(j!=i/j): 13 | x=x+int(i/j); 14 | lol[i]=x; 15 | for i in range (2,10001): 16 | if(lol[i]>1 and lol[i]!=i): 17 | if(i==lol[lol[i]]): 18 | ct=ct+i; 19 | print(ct) 20 | -------------------------------------------------------------------------------- /P23_Name_scores.py: -------------------------------------------------------------------------------- 1 | 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2 | s.sort(key=str.upper) 3 | ans=0 4 | print(s[937]) 5 | for i in range(0,len(s)): 6 | x=0; 7 | for j in range (0,len(s[i])): 8 | x=x+ord(s[i][j])-64 9 | ans=ans+(i+1)*x 10 | print(ans) 11 | 12 | -------------------------------------------------------------------------------- /P25_Hundred_Digit_fibo.py: -------------------------------------------------------------------------------- 1 | f1=1; 2 | f2=1; 3 | f3=2 4 | k=2; 5 | tst=10**999 6 | while(1): 7 | f3=f1+f2 8 | f1=f2 9 | f2=f3 10 | k=k+1; 11 | if(f3>=tst): 12 | break 13 | print(k) 14 | -------------------------------------------------------------------------------- /P26_Reciprocal_cycles.py: -------------------------------------------------------------------------------- 1 | m=0 2 | ind=0; 3 | for i in range(2,1000): 4 | pls=[0]*10000 5 | x=1; 6 | for k in range (0,10000): 7 | x=x*10 8 | if(pls[x%i]==1): 9 | break 10 | pls[x%i]=1 11 | x=x%i 12 | if(k>m): 13 | ind=i 14 | m=k 15 | print(ind) 16 | 17 | -------------------------------------------------------------------------------- /P27_Quadratic_Primes.py: -------------------------------------------------------------------------------- 1 | prime=[0]*100001 2 | for i in range(2,100001): 3 | if(prime[i]==0): 4 | for j in range (i+i,100001,i): 5 | prime[j]=1; 6 | prm=[] 7 | for i in range(2,1001): 8 | if(prime[i]==0): 9 | prm.append(i); 10 | m=0 11 | res=0 12 | for i in range (1,1001): 13 | a1=i 14 | for j in prm: 15 | x=1 16 | k=j; 17 | while(prime[k]==0): 18 | k=x*x+x*i+j; 19 | x=x+1; 20 | if(x>m): 21 | m=x 22 | res=i*j 23 | x=1 24 | k=j; 25 | while(prime[k]==0): 26 | k=abs(x*x+x*i-j); 27 | x=x+1; 28 | if(x>m): 29 | m=x 30 | res=i*j*-1 31 | a1=-1*i 32 | for j in prm: 33 | x=1 34 | k=j; 35 | while(prime[k]==0): 36 | k=abs(x*x+x*a1+j); 37 | x=x+1; 38 | if(x>m): 39 | m=x 40 | res=i*j*-1 41 | x=1 42 | k=j; 43 | while(prime[k]==0): 44 | k=abs(x*x+x*a1-j); 45 | x=x+1; 46 | if(x>m): 47 | m=x 48 | res=i*j 49 | print(m,res) 50 | 51 | -------------------------------------------------------------------------------- /P28_Number_Spiral_Diagonals.py: -------------------------------------------------------------------------------- 1 | x=1 2 | val=1 3 | for i in range (1,501): 4 | for j in range (1,5): 5 | val=val+2*i 6 | x=val+x 7 | print(val) 8 | print(x) 9 | -------------------------------------------------------------------------------- /P30_Digit_fifth_Powers.py: -------------------------------------------------------------------------------- 1 | n=0; 2 | po=[] 3 | for i in range(0,11): 4 | po.append(int(i**5)) 5 | for i in range (10,300001): 6 | k=i 7 | lol=0; 8 | while(k>0): 9 | x=int(k%10); 10 | lol=lol+po[x] 11 | k=k//10 12 | if(lol==i): 13 | n=n+i 14 | print(n) 15 | -------------------------------------------------------------------------------- /P31_Coin_Sums.py: -------------------------------------------------------------------------------- 1 | coin=[1,2,5,10,20,50,100,200] 2 | dp=[0]*1000 3 | dp[0]=1; 4 | for i in range(0,8): 5 | for j in range(coin[i],201): 6 | dp[j]=dp[j]+dp[j-coin[i]] 7 | print (dp[200]) 8 | -------------------------------------------------------------------------------- /P32_Pandigital_Products.py: -------------------------------------------------------------------------------- 1 | def pan(x): 2 | dig=[0]*10 3 | while(x): 4 | y=x%10 5 | dig[y]=dig[y]+1 6 | x=x//10 7 | if(dig[0]>0): 8 | return 0 9 | for i in range (1,10): 10 | if(dig[i]!=1): 11 | return 0 12 | return 1 13 | ls=[] 14 | for i in range (1,4): 15 | j1=10**(i-1) 16 | j=10**i 17 | for x in range (j1,j): 18 | lt=10**(5-i) 19 | for y in range(x,lt): 20 | k=x; 21 | res=0; 22 | while(k): 23 | res=res*10+k%10; 24 | k=k//10; 25 | k=y 26 | while(k): 27 | res=res*10+k%10; 28 | k=k//10; 29 | k=x*y 30 | while(k): 31 | res=res*10+k%10; 32 | k=k//10; 33 | ck=pan(res) 34 | if(ck==1): 35 | ls.append(x*y) 36 | print(*ls,sep=' ') 37 | print(sum(set(ls))) 38 | 39 | -------------------------------------------------------------------------------- /P33_Digit_Cancel.py: -------------------------------------------------------------------------------- 1 | import math 2 | prod1=1; 3 | prod2=1; 4 | for i in range (1,100): 5 | for j in range (i+1,100): 6 | #print(prod) 7 | n1=i%10; 8 | n2=i//10 9 | d1=j%10 10 | d2=j//10 11 | x=math.gcd(i,j) 12 | a1=i//x; 13 | a2=j//x 14 | if(n1==0 or d1==0 or n2==0 or d2==0): 15 | continue 16 | if(n1==d1): 17 | x=math.gcd(n2,d2) 18 | t1=n2//x 19 | t2=d2//x 20 | if(a1==t1 and a2==t2): 21 | prod1=prod1*a1 22 | prod2=prod2*a2 23 | continue 24 | if(n1==d2): 25 | x=math.gcd(n2,d1) 26 | t1=n2//x 27 | t2=d1//x 28 | if(a1==t1 and a2==t2): 29 | prod1=prod1*a1 30 | prod2=prod2*a2 31 | continue 32 | if(n2==d1): 33 | x=math.gcd(n1,d2) 34 | t1=n1//x 35 | t2=d2//x 36 | if(a1==t1 and a2==t2): 37 | prod1=prod1*a1 38 | prod2=prod2*a2 39 | continue 40 | if(n2==d2): 41 | x=math.gcd(n1,d1) 42 | t1=n1//x 43 | t2=d1//x 44 | if(a1==t1 and a2==t2): 45 | prod1=prod1*a1 46 | prod2=prod2*a2 47 | continue 48 | x=math.gcd(prod1,prod2) 49 | prod1=prod1/x 50 | prod2=prod2/x 51 | print(prod2) 52 | -------------------------------------------------------------------------------- /P34_Digit_Factorials.py: -------------------------------------------------------------------------------- 1 | fac=[1]*11 2 | fac[0]=1 3 | for i in range(1,10): 4 | fac[i]=fac[i-1]*i 5 | s=0 6 | for i in range(10,100001): 7 | x=i 8 | res=0 9 | while(x): 10 | res= res+fac[x%10] 11 | x=x//10 12 | if(i==res): 13 | s=s+i 14 | print(s) 15 | -------------------------------------------------------------------------------- /P357_Prime_Generating_int.py: -------------------------------------------------------------------------------- 1 | import math 2 | n=100000001 3 | pr=[1]*n 4 | pr[1]=0 5 | pr[0]=0 6 | for i in range(2,n): 7 | if(pr[i]==1): 8 | for j in range(i+i,n,i): 9 | pr[j]=0; 10 | sm=1 11 | val=[1]*n 12 | for i in range(2,n): 13 | if(pr[i]==1): 14 | x=i*i; 15 | for j in range(x,n,x): 16 | val[j]=0; 17 | for i in range(2,n-1,2): 18 | if(val[i]==1): 19 | if(pr[i+1]==1 and pr[(i//2)+2]==1): 20 | lt=int(math.sqrt(i)) 21 | fl=1 22 | for j in range(2,lt+1): 23 | if(i%j==0): 24 | if(pr[j+i//j]==0): 25 | fl=0; 26 | break; 27 | if(fl==1): 28 | sm=sm+i 29 | print(sm) 30 | -------------------------------------------------------------------------------- /P35_Circular_Primes.py: -------------------------------------------------------------------------------- 1 | lt=1000000 2 | prm=[1]*lt 3 | for i in range(2,lt): 4 | if(prm[i]==1): 5 | for j in range(i+i,lt,i): 6 | prm[j]=0 7 | ct=0 8 | for i in range(2,lt): 9 | x=i 10 | dc=0 11 | if(prm[i]==1): 12 | while(x): 13 | x=x//10 14 | dc=dc+1 15 | x=i; 16 | f=0 17 | for j in range (0,dc): 18 | y=x%10 19 | x=y*10**dc+x 20 | x=x//10 21 | if(prm[x]==0): 22 | f=1; 23 | break 24 | if(f==0): 25 | ct=ct+1 26 | print(ct) 27 | 28 | 29 | -------------------------------------------------------------------------------- /P36_Double_Palindrome.py: -------------------------------------------------------------------------------- 1 | ct=0 2 | for i in range (1,1000000): 3 | x=str(i)[::-1] 4 | x1=str(i) 5 | y=str(bin(i))[2:] 6 | y1=str(y)[::-1] 7 | if(y==y1 and x==x1): 8 | ct=ct+i 9 | print(ct) 10 | -------------------------------------------------------------------------------- /P37_Truncatable _Primes.py: -------------------------------------------------------------------------------- 1 | lt=1000000 2 | prm=[1]*lt 3 | prm[0]=0 4 | prm[1]=0 5 | for i in range(2,lt): 6 | if(prm[i]==1): 7 | for j in range(i+i,lt,i): 8 | prm[j]=0 9 | ct=0 10 | for i in range (10,lt): 11 | f=0 12 | x=i 13 | while(x): 14 | if(prm[x]==0): 15 | f=1 16 | break 17 | x=x//10 18 | x=i 19 | while(x): 20 | if(prm[x]==0): 21 | f=1 22 | break 23 | x=int(str(x)[::-1]) 24 | x=x//10 25 | x=int(str(x)[::-1]) 26 | 27 | if(f==0): 28 | print(i) 29 | ct=ct+i 30 | print(ct) 31 | -------------------------------------------------------------------------------- /P387_Harshad_Numbers.py: -------------------------------------------------------------------------------- 1 | import math; 2 | def prm(nm): 3 | f=0; 4 | if(nm==1): 5 | return 1; 6 | ck=int(math.sqrt(nm)) 7 | for i in range (2,ck+1): 8 | if((nm%i)==0): 9 | f=1; 10 | break; 11 | return f; 12 | def fn(x,s): 13 | global ct,n 14 | n=100000000000000 15 | if(x>(n/10)): 16 | return; 17 | if(x<10): 18 | ct=0 19 | tm=int(x/s); 20 | if(prm(tm)==0): 21 | for i in range(10): 22 | y=10*x+i 23 | if(y<=n): 24 | if(prm(y)==0): 25 | ct=ct+y 26 | for i in range(10): 27 | y=x*10+i 28 | sm=s+i; 29 | if((y%sm)==0): 30 | fn(y,sm) 31 | fn(1,1) 32 | ans=ct; 33 | for j in range(2,10,2): 34 | fn(j,j) 35 | print(j,ct) 36 | ans=ans+ct 37 | print(ans) -------------------------------------------------------------------------------- /P38_Pandigital_Multiples.py: -------------------------------------------------------------------------------- 1 | def pan(x): 2 | dig=[0]*10 3 | while(x): 4 | y=x%10 5 | dig[y]=dig[y]+1 6 | x=x//10 7 | if(dig[0]>0): 8 | return 0 9 | for i in range (1,10): 10 | if(dig[i]!=1): 11 | return 0 12 | return 1 13 | mx=0 14 | x="" 15 | lt=10000000000 16 | for i in range(1,100000): 17 | x=i 18 | s="" 19 | j=0 20 | while(jmx): 25 | mx=j 26 | x=x+i 27 | print(mx) 28 | -------------------------------------------------------------------------------- /P39_Integer_Triangles.py: -------------------------------------------------------------------------------- 1 | ck=[0]*10000 2 | for x in range(1,1001): 3 | if(x%20==0): 4 | print(x) 5 | for a in range(1,x): 6 | for b in range(1,x-a): 7 | c=x-a-b 8 | if(c<=0): 9 | break 10 | if((a*a+b*b)==c*c): 11 | ck[x]=ck[x]+1 12 | ans=0 13 | for i in range(1,1001): 14 | if(ck[i]>ck[ans]): 15 | ans=i 16 | print(ans) 17 | -------------------------------------------------------------------------------- /P40_Champernoven's_Constant.py: -------------------------------------------------------------------------------- 1 | k=0 2 | ans=1; 3 | j=0; 4 | for i in range(1,1000000): 5 | x=str(i) 6 | for m in range(len(x)): 7 | k=k+1 8 | s=int(x[m]) 9 | if(k==10**j): 10 | j=j+1 11 | ans=ans*s 12 | if(k>1000000): 13 | break 14 | print(ans) 15 | -------------------------------------------------------------------------------- /P41_Pandigital_Prime.py: -------------------------------------------------------------------------------- 1 | from itertools import permutations 2 | import math 3 | perms = [''.join(p) for p in permutations('1234567')] 4 | ct=0 5 | for i in perms: 6 | x=int(i) 7 | y=int(math.sqrt(x)) 8 | f=0 9 | for j in range(2,y+1): 10 | if(x%j==0): 11 | f=1 12 | break 13 | if(f==0 and x>ct): 14 | ct=x 15 | print(ct) 16 | -------------------------------------------------------------------------------- /P42_coded_triangle.py: -------------------------------------------------------------------------------- 1 | tr=[0]*10000 2 | 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ADE","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"] 3 | for i in s: 4 | t=0 5 | for j in range (len(i)): 6 | t=t+ord(i[j])-64 7 | tr[t]=tr[t]+1 8 | ct=0 9 | cur=0 10 | for i in range(1,1000): 11 | cur=cur+i 12 | if(cur>=10000): 13 | break 14 | ct=ct+tr[cur] 15 | print(ct) 16 | -------------------------------------------------------------------------------- /P43_Substring_Divisibility.py: -------------------------------------------------------------------------------- 1 | def pan(x): 2 | dig=[0]*10 3 | while(x): 4 | y=x%10 5 | dig[y]=dig[y]+1 6 | x=x//10 7 | if(dig[0]>0): 8 | return 0 9 | for i in range (1,10): 10 | if(dig[i]!=1): 11 | return 0 12 | return 1 13 | 14 | us=[0,1,2,3,4,5,6,7,8,9] 15 | s=[] 16 | for d1 in us: 17 | us.remove(d1) 18 | for d2 in us: 19 | #print(d1,d2,sep=' ') 20 | us.remove(d2) 21 | for d3 in us: 22 | us.remove(d3) 23 | for d4 in us: 24 | if((d2*100+d3*10+d4)%2==0): 25 | us.remove(d4) 26 | for d5 in us: 27 | if((d3*100+d4*10+d5)%3==0): 28 | us.remove(d5) 29 | for d6 in us: 30 | if((d4*100+d5*10+d6)%5==0): 31 | us.remove(d6) 32 | for d7 in us: 33 | if((d5*100+d6*10+d7)%7==0): 34 | us.remove(d7) 35 | for d8 in us: 36 | if((d6*100+d7*10+d8)%11==0): 37 | us.remove(d8) 38 | for d9 in us: 39 | if((d7*100+d8*10+d9)%13==0): 40 | us.remove(d9) 41 | for d10 in us: 42 | if((d8*100+d9*10+d10)%17==0): 43 | s.append(str(d10)+str(d9)+str(d8)+str(d7)+str(d6)+str(d5)+str(d4)+str(d3)+str(d2)+str(d1)) 44 | us.append(d9) 45 | us.sort() 46 | us.append(d8) 47 | us.sort() 48 | us.append(d7) 49 | us.sort() 50 | us.append(d6) 51 | us.sort() 52 | us.append(d5) 53 | us.sort() 54 | us.append(d4) 55 | us.sort() 56 | us.append(d3) 57 | us.sort() 58 | us.append(d2) 59 | us.sort() 60 | us.append(d1) 61 | us.sort() 62 | for i in range(len(s)): 63 | s[i]=int(s[i][::-1]) 64 | print(sum(s)) 65 | 66 | 67 | 68 | -------------------------------------------------------------------------------- /P44_Pentagon_Numbers.py: -------------------------------------------------------------------------------- 1 | pe=[] 2 | for i in range(1,5000): 3 | pe.append(i*(3*i-1)//2) 4 | a=0 5 | pex=set(pe) 6 | for i in range (len(pe)): 7 | for j in range (i-1,0,-1): 8 | if((pe[i]+pe[j]in pex) and (pe[i]-pe[j] in pex)): 9 | a=pe[i]-pe[j] 10 | break 11 | if(a!=0): 12 | break 13 | print(a) 14 | -------------------------------------------------------------------------------- /P45_Triangular_Pent_Hex.py: -------------------------------------------------------------------------------- 1 | t=set() 2 | p=set() 3 | h=set() 4 | for i in range(1,100000): 5 | t.add(i*(i+1)//2) 6 | p.add(i*(3*i-1)//2) 7 | h.add(i*(2*i-1)) 8 | k=t.intersection(p) 9 | k=k.intersection(h) 10 | print(k) 11 | -------------------------------------------------------------------------------- /P46_Goldbach's_Conjecture.py: -------------------------------------------------------------------------------- 1 | lt=10000 2 | pr=[1]*lt 3 | ck=[0]*lt 4 | sq=[] 5 | for i in range(2,lt): 6 | if(pr[i]==1): 7 | for j in range(i+i,lt,i): 8 | pr[j]=0 9 | for i in range (1,10000): 10 | sq.append(2*i*i) 11 | for i in range(2,lt): 12 | if(pr[i]==1): 13 | for j in range(0,10000): 14 | x=i+sq[j] 15 | if(x>=lt): 16 | break 17 | ck[x]=1 18 | ck[i]=1 19 | for i in range(2,lt): 20 | if(i%2==1 and ck[i]==0): 21 | ans=i 22 | break 23 | print(ans) 24 | -------------------------------------------------------------------------------- /P47_Distinct_Prime_factors.py: -------------------------------------------------------------------------------- 1 | lt=1000000 2 | li=[] 3 | prm=[0]*lt 4 | for i in range(2,lt): 5 | if(prm[i]==0): 6 | for j in range(i+i,lt,i): 7 | prm[j]=prm[j]+1 8 | for i in range(2,lt): 9 | if(prm[i]==prm[i+1]==prm[i+2]==prm[i+3]==4): 10 | break 11 | print(i) 12 | -------------------------------------------------------------------------------- /P48_self_Powers.py: -------------------------------------------------------------------------------- 1 | mo=10000000000 2 | lol=0 3 | for i in range(1,1000): 4 | x=1 5 | for j in range(1,i+1): 6 | x=(x*i)%mo 7 | lol=(lol+x)%mo 8 | print(lol) 9 | 10 | -------------------------------------------------------------------------------- /P49_Prime_Permutations.py: -------------------------------------------------------------------------------- 1 | from itertools import permutations 2 | lt=10000 3 | pr=[0]*10000 4 | for i in range(2,lt): 5 | if(pr[i]==0): 6 | for j in range(i+i,lt,i): 7 | pr[j]=1 8 | for i in range(1000,10000): 9 | if(pr[i]==0): 10 | x=str(i) 11 | lol=[] 12 | for p in permutations(x): 13 | p=''.join(p) 14 | if(pr[int(p)]==0): 15 | lol.append(int(p)) 16 | zz=set(lol) 17 | lol=list(zz) 18 | lol.sort() 19 | for m in range (len(lol)): 20 | for n in range(m+1,len(lol)): 21 | for o in range(n+1,len(lol)): 22 | if(lol[o]-lol[n]==lol[n]-lol[m]): 23 | print(lol[m],lol[n],lol[o],sep=' ') 24 | -------------------------------------------------------------------------------- /P50_consecutive_Prime_sum.py: -------------------------------------------------------------------------------- 1 | lt=1000000 2 | prm=[1]*lt 3 | ck=[0]*lt 4 | prm[0]=0 5 | prm[1]=0 6 | for i in range(2,lt): 7 | if(prm[i]==1): 8 | for j in range(i+i,lt,i): 9 | prm[j]=0 10 | li=[] 11 | for i in range(1,lt): 12 | if(prm[i]==1): 13 | li.append(i) 14 | for i in range(len(li)): 15 | x=0 16 | for j in range(i,len(li)): 17 | x=x+li[j] 18 | if(x>=lt): 19 | break 20 | if(ck[x]ck[x]): 25 | x=i 26 | print(x) 27 | 28 | -------------------------------------------------------------------------------- /P52_Permuted_Multiples.py: -------------------------------------------------------------------------------- 1 | ma=0 2 | for i in range(1,10000000): 3 | j=str(i) 4 | t=''.join(sorted(j)) 5 | f=0 6 | for k in range(2,7): 7 | x=''.join(sorted(str(i*k))) 8 | if(x!=t): 9 | f=1 10 | break; 11 | if(f==0): 12 | break 13 | print(i) 14 | -------------------------------------------------------------------------------- /P53_Combinatorial_Selection.py: -------------------------------------------------------------------------------- 1 | f=[0]*1000 2 | f[0]=1; 3 | for i in range (1,101): 4 | f[i]=f[i-1]*i 5 | ct=0 6 | for n in range (1,101): 7 | for r in range(1,n+1): 8 | c=f[n]/f[r] 9 | c=c/f[n-r] 10 | if(c>1000000): 11 | ct=ct+1 12 | print(ct) 13 | -------------------------------------------------------------------------------- /P55_Lychreal_Numbers.py: -------------------------------------------------------------------------------- 1 | ct=0 2 | for i in range(1,10000): 3 | x=str(i) 4 | for j in range(51): 5 | t=x[::-1] 6 | z=int(x)+int(t) 7 | if(str(z)[::-1]==str(z)): 8 | break 9 | x=str(z) 10 | if(j>=49): 11 | ct=ct+1; 12 | print(ct) 13 | -------------------------------------------------------------------------------- /P56_Power_sums.py: -------------------------------------------------------------------------------- 1 | m=0 2 | for i in range(1,100): 3 | for j in range(1,100): 4 | t=sum([int(char) for char in str(i**j)]) 5 | if(t>m): 6 | m=t 7 | print(m) 8 | -------------------------------------------------------------------------------- /P57_Square_Root_Convergents.py: -------------------------------------------------------------------------------- 1 | from fractions import Fraction 2 | ct=0 3 | x=Fraction(3,2) 4 | for i in range(1000): 5 | y=1/(Fraction(1,1)+x)+Fraction(1,1) 6 | x=y 7 | if(len(str(y.numerator))>len(str(y.denominator))): 8 | ct=ct+1 9 | print(ct) 10 | -------------------------------------------------------------------------------- /P58_Spiral_Primes.py: -------------------------------------------------------------------------------- 1 | import math 2 | x=0 3 | val=1 4 | for i in range (1,50001): 5 | for j in range (1,5): 6 | val=val+2*i 7 | y=int(math.sqrt(val)) 8 | f=0 9 | for k in range(2,y+1): 10 | if(val%k==0): 11 | f=1 12 | break 13 | if(f==0): 14 | x=x+1 15 | t=(i)*4+1; 16 | #print(x,t,sep=' ') 17 | if(x/t<0.1): 18 | break 19 | print(x,t) 20 | print(2*i+1) 21 | -------------------------------------------------------------------------------- /P59_XOR_Decryption.py: -------------------------------------------------------------------------------- 1 | a=[79,59,12,2,79,35,8,28,20,2,3,68,8,9,68,45,0,12,9,67,68,4,7,5,23,27,1,21,79,85,78,79,85,71,38,10,71,27,12,2,79,6,2,8,13,9,1,13,9,8,68,19,7,1,71,56,11,21,11,68,6,3,22,2,14,0,30,79,1,31,6,23,19,10,0,73,79,44,2,79,19,6,28,68,16,6,16,15,79,35,8,11,72,71,14,10,3,79,12,2,79,19,6,28,68,32,0,0,73,79,86,71,39,1,71,24,5,20,79,13,9,79,16,15,10,68,5,10,3,14,1,10,14,1,3,71,24,13,19,7,68,32,0,0,73,79,87,71,39,1,71,12,22,2,14,16,2,11,68,2,25,1,21,22,16,15,6,10,0,79,16,15,10,22,2,79,13,20,65,68,41,0,16,15,6,10,0,79,1,31,6,23,19,28,68,19,7,5,19,79,12,2,79,0,14,11,10,64,27,68,10,14,15,2,65,68,83,79,40,14,9,1,71,6,16,20,10,8,1,79,19,6,28,68,14,1,68,15,6,9,75,79,5,9,11,68,19,7,13,20,79,8,14,9,1,71,8,13,17,10,23,71,3,13,0,7,16,71,27,11,71,10,18,2,29,29,8,1,1,73,79,81,71,59,12,2,79,8,14,8,12,19,79,23,15,6,10,2,28,68,19,7,22,8,26,3,15,79,16,15,10,68,3,14,22,12,1,1,20,28,72,71,14,10,3,79,16,15,10,68,3,14,22,12,1,1,20,28,68,4,14,10,71,1,1,17,10,22,71,10,28,19,6,10,0,26,13,20,7,68,14,27,74,71,89,68,32,0,0,71,28,1,9,27,68,45,0,12,9,79,16,15,10,68,37,14,20,19,6,23,19,79,83,71,27,11,71,27,1,11,3,68,2,25,1,21,22,11,9,10,68,6,13,11,18,27,68,19,7,1,71,3,13,0,7,16,71,28,11,71,27,12,6,27,68,2,25,1,21,22,11,9,10,68,10,6,3,15,27,68,5,10,8,14,10,18,2,79,6,2,12,5,18,28,1,71,0,2,71,7,13,20,79,16,2,28,16,14,2,11,9,22,74,71,87,68,45,0,12,9,79,12,14,2,23,2,3,2,71,24,5,20,79,10,8,27,68,19,7,1,71,3,13,0,7,16,92,79,12,2,79,19,6,28,68,8,1,8,30,79,5,71,24,13,19,1,1,20,28,68,19,0,68,19,7,1,71,3,13,0,7,16,73,79,93,71,59,12,2,79,11,9,10,68,16,7,11,71,6,23,71,27,12,2,79,16,21,26,1,71,3,13,0,7,16,75,79,19,15,0,68,0,6,18,2,28,68,11,6,3,15,27,68,19,0,68,2,25,1,21,22,11,9,10,72,71,24,5,20,79,3,8,6,10,0,79,16,8,79,7,8,2,1,71,6,10,19,0,68,19,7,1,71,24,11,21,3,0,73,79,85,87,79,38,18,27,68,6,3,16,15,0,17,0,7,68,19,7,1,71,24,11,21,3,0,71,24,5,20,79,9,6,11,1,71,27,12,21,0,17,0,7,68,15,6,9,75,79,16,15,10,68,16,0,22,11,11,68,3,6,0,9,72,16,71,29,1,4,0,3,9,6,30,2,79,12,14,2,68,16,7,1,9,79,12,2,79,7,6,2,1,73,79,85,86,79,33,17,10,10,71,6,10,71,7,13,20,79,11,16,1,68,11,14,10,3,79,5,9,11,68,6,2,11,9,8,68,15,6,23,71,0,19,9,79,20,2,0,20,11,10,72,71,7,1,71,24,5,20,79,10,8,27,68,6,12,7,2,31,16,2,11,74,71,94,86,71,45,17,19,79,16,8,79,5,11,3,68,16,7,11,71,13,1,11,6,1,17,10,0,71,7,13,10,79,5,9,11,68,6,12,7,2,31,16,2,11,68,15,6,9,75,79,12,2,79,3,6,25,1,71,27,12,2,79,22,14,8,12,19,79,16,8,79,6,2,12,11,10,10,68,4,7,13,11,11,22,2,1,68,8,9,68,32,0,0,73,79,85,84,79,48,15,10,29,71,14,22,2,79,22,2,13,11,21,1,69,71,59,12,14,28,68,14,28,68,9,0,16,71,14,68,23,7,29,20,6,7,6,3,68,5,6,22,19,7,68,21,10,23,18,3,16,14,1,3,71,9,22,8,2,68,15,26,9,6,1,68,23,14,23,20,6,11,9,79,11,21,79,20,11,14,10,75,79,16,15,6,23,71,29,1,5,6,22,19,7,68,4,0,9,2,28,68,1,29,11,10,79,35,8,11,74,86,91,68,52,0,68,19,7,1,71,56,11,21,11,68,5,10,7,6,2,1,71,7,17,10,14,10,71,14,10,3,79,8,14,25,1,3,79,12,2,29,1,71,0,10,71,10,5,21,27,12,71,14,9,8,1,3,71,26,23,73,79,44,2,79,19,6,28,68,1,26,8,11,79,11,1,79,17,9,9,5,14,3,13,9,8,68,11,0,18,2,79,5,9,11,68,1,14,13,19,7,2,18,3,10,2,28,23,73,79,37,9,11,68,16,10,68,15,14,18,2,79,23,2,10,10,71,7,13,20,79,3,11,0,22,30,67,68,19,7,1,71,8,8,8,29,29,71,0,2,71,27,12,2,79,11,9,3,29,71,60,11,9,79,11,1,79,16,15,10,68,33,14,16,15,10,22,73] 2 | for i in range (97,123): 3 | for j in range(97,123): 4 | for k in range(97,123): 5 | x=[i,j,k]; 6 | f=0; 7 | l=0; 8 | sum=0 9 | s="" 10 | for m in range(len(a)): 11 | t=a[m]^x[l] 12 | l=(l+1)%3; 13 | s=s+(chr(t)) 14 | sum=sum+t 15 | if(t<32 or t>122): 16 | f=1 17 | break 18 | if(f==0): 19 | print(sum) 20 | print(s) 21 | -------------------------------------------------------------------------------- /P63_Powerful_Digit_Counts.py: -------------------------------------------------------------------------------- 1 | sum=0; 2 | for i in range (1,100): 3 | f=0; 4 | for j in range(1,10): 5 | lol=j**i; 6 | if(len(str(lol))==i): 7 | sum=sum+1; 8 | print(sum) 9 | -------------------------------------------------------------------------------- /P69_TotientMax.py: -------------------------------------------------------------------------------- 1 | # your code goes here 2 | n=1000001; 3 | #n=10 4 | sv=[1]*n; 5 | pr=[1]*n; 6 | for i in range (1,n): 7 | sv[i]=i; 8 | for i in range(2,n): 9 | if(pr[i]==1): 10 | x=(1-(1/i)) 11 | for j in range(i,n,i): 12 | pr[j]=0; 13 | sv[j]=sv[j]*x 14 | sv[i]=i/sv[i] 15 | sv[1]=0; 16 | z=1 17 | for i in range(2,n): 18 | #print(i,sv[i],sep=' ') 19 | if(sv[i]>sv[z]): 20 | z=i; 21 | print(z) -------------------------------------------------------------------------------- /P71_Ordered_Fractions.py: -------------------------------------------------------------------------------- 1 | # your code goes here 2 | # your code goes here 3 | import math 4 | fn=3/7; 5 | #print(fn) 6 | cls=0; 7 | ans=0; 8 | n=1000001 9 | #n=8 10 | for i in range(1,n): 11 | nm=fn*i; 12 | dn=i; 13 | x=int(math.floor(nm)); 14 | cur=x/dn 15 | #print(i,cur,sep=' ') 16 | if(curcls and x0): 8 | lol=lol+(k%10)*(k%10) 9 | k=k//10; 10 | if(lol==1): 11 | ck[x]=1; 12 | elif(lol==89): 13 | ck[x]=89; 14 | else: 15 | ck[x]=pls(lol) 16 | return ck[x] 17 | for i in range(1,10000000): 18 | if(ck[i]==0): 19 | ck[i]=pls(i) 20 | print(ck.count(89)) 21 | -------------------------------------------------------------------------------- /P97_Large non-Mersenne prime.py: -------------------------------------------------------------------------------- 1 | x=pow(2,7830457,10000000000); 2 | x=(x*28433)%10000000000; 3 | x=(x+1)%10000000000; 4 | print(x) 5 | -------------------------------------------------------------------------------- /P99_Largest_Exp.py: -------------------------------------------------------------------------------- 1 | import math 2 | # your code goes here 3 | n=1000; 4 | mx=0; 5 | ind=0 6 | tst=10000000000 7 | for i in range(n): 8 | x=[int(j) for j in input().split(',')] 9 | tmp=math.log(tst,x[0]); 10 | lol=x[1]/tmp; 11 | if(lol>mx): 12 | mx=lol 13 | ind=i+1 14 | print(ind) -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # ProjectEuler 2 | My project Euler solutions 3 | 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