Added solutions for N=100-110

100_arranged_probability.py

@@ -0,0 +1,13 @@
+#!/usr/bin/env python3
+
+lim = 10**12
+x, y = 3, 1
+blue = 3
+total  = 4
+
+while total <= lim:
+    x, y = 3*x + 8*y, 3*y + x
+    blue = (2*y + x + 1) // 2
+    total = (4*y + x + 1) // 2
+
+print(blue)

101_optimum_polynomials.py

@@ -0,0 +1,27 @@
+#!/usr/bin/env python3
+
+CFS = [1, -1]*5 + [1]
+
+def main(cfs):
+    seq = getseq(cfs)
+    py  = pyramid(seq)
+    return sum(op(n, py) for n in range(1, len(cfs)))
+
+def getseq(cfs):
+    return [sum(c*n**pw for pw, c in enumerate(cfs))
+            for n in range(1, len(cfs))]
+
+def pyramid(seq):
+    r = [seq]
+    for i in range(len(seq)-1):
+        lvl = []
+        for j in range(len(r[i])-1):
+            lvl.append(r[i][j+1] - r[i][j])
+        r.append(lvl)
+    return r
+
+def op(n, py):
+    return sum(py[i][n-i-1] for i in range(n))
+
+#print(main([0,0,0,1]))
+print(main(CFS))

102_triangle_containment.py

@@ -0,0 +1,23 @@
+#!/usr/bin/env python3
+
+# Calculate area of triangle and compare to areas
+# of triangles with one vertex = origin
+# better solution -> check sign of cross products
+
+def main():
+    tr = parse("data/102_triangles.txt")
+    return len([0 for p in tr if areaTR(p) == areaOG(0,2,p) + areaOG(0,4,p) + areaOG(2,4,p)])
+
+def areaTR(p):  #triangle area
+    return abs(p[0]*p[3] - p[0]*p[5] + 
+               p[2]*p[5] - p[2]*p[1] +
+               p[4]*p[1] - p[4]*p[3])
+
+def areaOG(a, b, p): #triangle with with a=0,0
+    return abs(p[a]*p[b+1] - p[b]*p[a+1])
+
+def parse(path):
+    with open(path) as f:
+        return [list(map(int, row.split(","))) for row in f.read()[:-1].split("\n")]
+
+print(main())

103_special_subset_sums_optimum.py

@@ -0,0 +1,46 @@
+#!/usr/bin/env python3
+
+def test(n, setsums):
+    newsums = [s+n for s in setsums] + setsums + [n]
+    if len(newsums) != len(set(newsums)):
+        return False
+    return newsums
+
+def search(left, right, length, best, setsums, lor, w): #left to right
+    if len(left + right) >= length:
+        if sum(left + right) < best:
+            #print left+right, sum(left+right)
+            for i, n in enumerate(left+right):
+                w[i] = n
+            return sum(left + right)
+        return best
+    hole = length - len(left + right) - 1
+    minsum = sum(left + right) + (hole*(hole+1))//2 + left[-1]*hole
+    if lor:
+        n = max(left[-1]+1, sum(right)-sum(left) + 1)
+        bound = right[0] - hole
+    else:
+        n = left[-1] + hole + 1
+        bound = best - minsum
+        if len(right) > 0 and right[0] < bound:
+            bound = right[0]
+    while n < bound and n < best - minsum - (n-left[-1])*hole*lor:
+        newsums = test(n, setsums)
+        if newsums:
+            best = search(left + [n]*lor,
+                          [n]*(not lor) + right,
+                          length, best, newsums, not lor, w)
+        n += 1
+    return best
+
+def base(length, best):
+    x = length//2 + length % 2
+    n = (x + 1 - length%2) * (x-1) + 1
+    n = 20
+    w = [0]*length
+    while n < best - (length-1)*length - n*(length-1):
+        best = search([n], [], length, best, [n], False, w)
+        n += 1
+    return "".join(map(str, w)), best
+
+print(base(7, 500)[0])

104_pandigital_fibonacci_ends.py

@@ -0,0 +1,25 @@
+#!/usr/bin/env python3
+
+from math import sqrt, log10
+
+def main():
+    k = 1
+    m    = 0
+    last = 1
+    gr    = (1 + sqrt(5)) / 2
+    first = gr*(1/sqrt(5))
+    while cond(str(int(first))[:9], str(last)):
+        last, m = (last+m)%10**9, last
+        first = gr*first
+        if first >= 10**9:
+            first /= 10
+        k += 1
+    return k, int(log10(gr)*k - log10(1/sqrt(5)) + 1/2.0)
+
+def cond(first, last):
+    a = len(set(last))  != 9
+    b = len(set(first)) != 9
+    c = '0' in first+last
+    return a or b or c
+
+print(main()[0])

105_special_subset_sums_testing.py

@@ -0,0 +1,21 @@
+#!/usr/bin/env python3
+
+def test(s):
+    if len(s) != len(set(s)):
+        return False
+    s.sort()
+    if sum(s[:len(s)//2 + len(s)%2]) <= sum(s[len(s)//2+1:]):
+        return False
+    setsums = []
+    for n in s:
+        setsums += [m+n for m in setsums] + [n]
+        if len(setsums) != len(set(setsums)):
+            return False
+    return True
+
+with open("data/105_sets.txt") as f:
+    r = f.read()
+
+sets = [list(map(int, line.split(','))) for line in r.split('\n')[:-1]]
+
+print(sum(sum(s) for s in sets if test(s)))

106_special_subset_sums_meta.py

@@ -0,0 +1,17 @@
+#!/usr/bin/env python3
+
+from math import factorial
+
+def bin(n, k):
+    if n < 0:
+        return 0
+    if n < k:
+        return 0
+    return factorial(n) // (factorial(n-k) * factorial(k))
+
+n = 12
+ms = 0
+for k in range(0, n//2 +1):
+    ms += bin(n, 2*k) * bin(2*k-1, k+1)
+
+print(ms)

107_minimal_network.py

@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+
+def parse(fname):
+    with open(fname) as f:
+        r = f.read()
+    r = [line.split(',') for line in r.split('\n')[:-1]]
+    weights = {a : [(b, int(w)) for b, w in enumerate(line)
+                                   if w!='-'
+                   ]
+                   for a, line in enumerate(r)
+              }
+    return weights
+
+def search(network, visited={0}):
+    if len(visited) == len(network):
+        return 0
+    edges = [(n2, w) for node in visited
+                   for n2, w in network[node]
+                   if n2 not in visited
+            ]
+    next, w = min(edges, key = lambda x: x[1])
+    return w + search(network, visited | {next})
+
+network = parse("data/107_network.txt")
+total_weight  = sum(w for node in network
+                     for _, w in network[node])
+total_weight //= 2
+min_weight    = search(network)
+
+print(total_weight - min_weight)

108_diophantine_reciprocals_I.py

@@ -0,0 +1,54 @@
+#!/usr/bin/env python3
+
+from lib import primegen
+from math import log
+from operator import mul
+from functools import reduce
+
+def calc(pows):
+    return (reduce(mul, (2*p + 1 for p in pows)) + 1) // 2
+
+def increment(i, pows):
+    n = 0
+    if i < len(pows):
+        n = pows[i]
+    return [n + 1] * (i+1) + pows[i+1:]
+
+def val(pows):
+    return sum(p*v for p, v in zip(pows, vals))
+
+def fpwof2(pows, n):
+    if len(pows) == 1:
+        return n-1
+    r = (2*n - 1) // reduce(mul, (2*p + 1 for p in pows[1:]))
+    r = (r - 1) // 2
+    while calc([r] + pows[1:]) < n:
+        r += 1
+    return r
+
+N = 10 ** 3
+
+primes = list(primegen(100))
+vals   = [log(p) / log(2) for p in primes]
+
+i = 0
+pows = [0]
+best = fpwof2(pows, N)
+best_pows = None
+
+while not (val(pows) >= best and sum(pows) == len(pows)):
+    if not i:
+        pows[0] = fpwof2(pows, N)
+        if len(pows) > 1 and pows[0] < pows[1]:
+            pows[0]  = pows[1]
+        if val(pows) < best:
+            best = val(pows)
+            best_pows = pows
+        i = 1
+    pows = increment(i, pows)
+    if val(pows) >= best:
+        i += 1
+    else:
+        i = 0
+
+print(reduce(mul, (n**pw for n, pw in zip(primes, best_pows))))

109_darts.py

@@ -0,0 +1,24 @@
+#!/usr/bin/env python3
+
+bull = [25]
+miss = [0]
+fields = list(range(1, 21))
+single = fields + bull
+double = [2*i for i in single] 
+treble  =[3*i for i in fields]
+
+regs = miss + single + double + treble
+regs.sort()
+
+count = 0
+score = 100
+
+for fst in double:
+    for i, sec in enumerate(regs):
+        if fst + 2*sec >= score:
+            break
+        for thd in regs[i:]:
+            if fst + sec + thd >= score:
+                break
+            count += 1
+print(count)

data/105_sets.txt

@@ -0,0 +1,100 @@
+81,88,75,42,87,84,86,65
+157,150,164,119,79,159,161,139,158
+673,465,569,603,629,592,584,300,601,599,600
+90,85,83,84,65,87,76,46
+165,168,169,190,162,85,176,167,127
+224,275,278,249,277,279,289,295,139
+354,370,362,384,359,324,360,180,350,270
+599,595,557,298,448,596,577,667,597,588,602
+175,199,137,88,187,173,168,171,174
+93,187,196,144,185,178,186,202,182
+157,155,81,158,119,176,152,167,159
+184,165,159,166,163,167,174,124,83
+1211,1212,1287,605,1208,1189,1060,1216,1243,1200,908,1210
+339,299,153,305,282,304,313,306,302,228
+94,104,63,112,80,84,93,96
+41,88,82,85,61,74,83,81
+90,67,84,83,82,97,86,41
+299,303,151,301,291,302,307,377,333,280
+55,40,48,44,25,42,41
+1038,1188,1255,1184,594,890,1173,1151,1186,1203,1187,1195
+76,132,133,144,135,99,128,154
+77,46,108,81,85,84,93,83
+624,596,391,605,529,610,607,568,604,603,453
+83,167,166,189,163,174,160,165,133
+308,281,389,292,346,303,302,304,300,173
+593,1151,1187,1184,890,1040,1173,1186,1195,1255,1188,1203
+68,46,64,33,60,58,65
+65,43,88,87,86,99,93,90
+83,78,107,48,84,87,96,85
+1188,1173,1256,1038,1187,1151,890,1186,1184,1203,594,1195
+302,324,280,296,294,160,367,298,264,299
+521,760,682,687,646,664,342,698,692,686,672
+56,95,86,97,96,89,108,120
+344,356,262,343,340,382,337,175,361,330
+47,44,42,27,41,40,37
+139,155,161,158,118,166,154,156,78
+118,157,164,158,161,79,139,150,159
+299,292,371,150,300,301,281,303,306,262
+85,77,86,84,44,88,91,67
+88,85,84,44,65,91,76,86
+138,141,127,96,136,154,135,76
+292,308,302,346,300,324,304,305,238,166
+354,342,341,257,348,343,345,321,170,301
+84,178,168,167,131,170,193,166,162
+686,701,706,673,694,687,652,343,683,606,518
+295,293,301,367,296,279,297,263,323,159
+1038,1184,593,890,1188,1173,1187,1186,1195,1150,1203,1255
+343,364,388,402,191,383,382,385,288,374
+1187,1036,1183,591,1184,1175,888,1197,1182,1219,1115,1167
+151,291,307,303,345,238,299,323,301,302
+140,151,143,138,99,69,131,137
+29,44,42,59,41,36,40
+348,329,343,344,338,315,169,359,375,271
+48,39,34,37,50,40,41
+593,445,595,558,662,602,591,297,610,580,594
+686,651,681,342,541,687,691,707,604,675,699
+180,99,189,166,194,188,144,187,199
+321,349,335,343,377,176,265,356,344,332
+1151,1255,1195,1173,1184,1186,1188,1187,1203,593,1038,891
+90,88,100,83,62,113,80,89
+308,303,238,300,151,304,324,293,346,302
+59,38,50,41,42,35,40
+352,366,174,355,344,265,343,310,338,331
+91,89,93,90,117,85,60,106
+146,186,166,175,202,92,184,183,189
+82,67,96,44,80,79,88,76
+54,50,58,66,31,61,64
+343,266,344,172,308,336,364,350,359,333
+88,49,87,82,90,98,86,115
+20,47,49,51,54,48,40
+159,79,177,158,157,152,155,167,118
+1219,1183,1182,1115,1035,1186,591,1197,1167,887,1184,1175
+611,518,693,343,704,667,686,682,677,687,725
+607,599,634,305,677,604,603,580,452,605,591
+682,686,635,675,692,730,687,342,517,658,695
+662,296,573,598,592,584,553,593,595,443,591
+180,185,186,199,187,210,93,177,149
+197,136,179,185,156,182,180,178,99
+271,298,218,279,285,282,280,238,140
+1187,1151,890,593,1194,1188,1184,1173,1038,1186,1255,1203
+169,161,177,192,130,165,84,167,168
+50,42,43,41,66,39,36
+590,669,604,579,448,599,560,299,601,597,598
+174,191,206,179,184,142,177,180,90
+298,299,297,306,164,285,374,269,329,295
+181,172,162,138,170,195,86,169,168
+1184,1197,591,1182,1186,889,1167,1219,1183,1033,1115,1175
+644,695,691,679,667,687,340,681,770,686,517
+606,524,592,576,628,593,591,584,296,444,595
+94,127,154,138,135,74,136,141
+179,168,172,178,177,89,198,186,137
+302,299,291,300,298,149,260,305,280,370
+678,517,670,686,682,768,687,648,342,692,702
+302,290,304,376,333,303,306,298,279,153
+95,102,109,54,96,75,85,97
+150,154,146,78,152,151,162,173,119
+150,143,157,152,184,112,154,151,132
+36,41,54,40,25,44,42
+37,48,34,59,39,41,40
+681,603,638,611,584,303,454,607,606,605,596

data/107_network.txt

@@ -0,0 +1,40 @@
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data/107_test.txt

@@ -0,0 +1,7 @@
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