# HG changeset patch
# User Dominic Cleal <dominic@computerkb.co.uk>
# Date 1228129021 0
# Node ID 1ca695e32f66ac93c323493b07adadb23cd712bf

Solutions from tungsten

diff -r 000000000000 -r 1ca695e32f66 keylog.txt
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/keylog.txt	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,50 @@
+319
+680
+180
+690
+129
+620
+762
+689
+762
+318
+368
+710
+720
+710
+629
+168
+160
+689
+716
+731
+736
+729
+316
+729
+729
+710
+769
+290
+719
+680
+318
+389
+162
+289
+162
+718
+729
+319
+790
+680
+890
+362
+319
+760
+316
+729
+380
+319
+728
+716
diff -r 000000000000 -r 1ca695e32f66 problem1.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem1.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,15 @@
+skips = [3,2,1,3,1,2,3]
+s = 0
+
+tot = 0
+i = 0
+
+while i<1000:
+	tot += i
+	i += skips[s]
+	s += 1
+	if s==len(skips):
+		s = 0
+
+print tot
+
diff -r 000000000000 -r 1ca695e32f66 problem10.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem10.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,21 @@
+import math
+
+primes = [ 2 ]
+
+def isPrime(test):
+	max = math.floor(math.sqrt(test))
+	t = 0
+	while t < len(primes) and primes[t] <= max:
+		if test % primes[t] == 0:
+			return False
+		t += 1
+	
+	return True
+
+i = 3
+while i < 2000000:
+	if isPrime(i):
+		primes.append(i)
+	i += 2
+
+print sum(primes)
diff -r 000000000000 -r 1ca695e32f66 problem14.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem14.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,25 @@
+def even(x): return x/2
+def odd(x): return 3*x + 1
+
+def fn(x):
+	if x % 2 == 0:
+		return even(x)
+	else:
+		return odd(x)
+
+def lookup(x, cache):
+	if not x in cache:
+		cache[x] = lookup(fn(x), cache) + 1
+	return cache[x]
+
+mx = 0
+ml = 0
+cache = { 1: 1 }
+for rx in range(1, 1000001):
+	l = lookup(rx, cache)
+	
+	if l > ml:
+		mx = rx
+		ml = l
+
+print "Best x is %d with len %d" % (mx, ml)
diff -r 000000000000 -r 1ca695e32f66 problem16.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem16.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,1 @@
+print sum([int(a) for a in str(2**1000)])
diff -r 000000000000 -r 1ca695e32f66 problem2.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem2.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,16 @@
+tot = 2
+f = [ 1, 2 ]
+
+while True:
+	f.append(f[0] + f[1])
+	f.pop(0)
+	f.append(f[0] + f[1])
+	f.pop(0)
+	e = f[0] + f[1]
+	if e>4000000:
+		break
+	tot += e
+	f.append(e)
+	f.pop(0)
+
+print tot
diff -r 000000000000 -r 1ca695e32f66 problem20.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem20.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,3 @@
+import operator
+f = reduce(operator.mul, range(2, 101))
+print sum([int(c) for c in str(f)])
diff -r 000000000000 -r 1ca695e32f66 problem4.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem4.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,18 @@
+import math
+
+def ispal(x):
+	s = str(x)
+	for i in range(0, int(len(s) / 2)):
+		if (s[i] != s[-i - 1]):
+			return False
+	return True
+
+r = range(1000, 99, -1)
+p = -1
+for a in r:
+	for b in r:
+		m = a*b
+		if ispal(m) and m > p:
+			print "Answer: %d x %d = %d (%s)" % (a,b,m, ispal(m))
+			p = m
+
diff -r 000000000000 -r 1ca695e32f66 problem48.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem48.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,3 @@
+s = sum([a**a for a in range(1,1001)])
+print s
+print str(s)[-10:]
diff -r 000000000000 -r 1ca695e32f66 problem5.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem5.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,17 @@
+import math
+
+m = 20
+
+divs = range(int(math.ceil(m / 2)) + 1, m)
+
+t = m
+while True:
+	for d in divs:
+		if t % d > 0:
+			break	
+	else:
+		print t
+		exit
+	t += m
+	
+
diff -r 000000000000 -r 1ca695e32f66 problem6.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem6.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,6 @@
+def sq(x): return x*x
+
+r = range(1,101);
+a = sum(map(sq, r));
+b = sq(sum(r));
+print (b-a)
diff -r 000000000000 -r 1ca695e32f66 problem7.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem7.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,21 @@
+import math
+
+primes = [ 2 ]
+
+def isPrime(test):
+	max = math.floor(math.sqrt(test))
+	t = 0
+	while t < len(primes) and primes[t] <= max:
+		if test % primes[t] == 0:
+			return False
+		t += 1
+	
+	return True
+
+i = 3
+while len(primes) < 10001:
+	if isPrime(i):
+		primes.append(i)
+	i += 2
+
+print primes.pop()
diff -r 000000000000 -r 1ca695e32f66 problem79.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem79.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,35 @@
+import sys
+
+class Code:
+	after = []
+	
+	def __init__(self, num, after):
+		self.num = num
+		self.after = after
+
+def code_cmp(a, b):
+	if a.num == b.num:
+		return 0
+	elif a.num in b.after:
+		return 1
+	elif b.num in a.after:
+		return -1
+	else:
+		return 0
+
+codes = []
+
+f = open("keylog.txt")
+try:
+	for line in f:
+		linecodes = []
+		for i in [int(i) for i in line.rstrip()]:
+			codes.append(Code(i, linecodes))
+			linecodes.append(i)
+finally:
+	f.close()
+
+print ''.join([str(c.num) for c in codes])
+codes.sort(code_cmp)
+print ''.join([str(c.num) for c in codes])
+
diff -r 000000000000 -r 1ca695e32f66 problem8.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem8.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,58 @@
+import sys
+
+
+num = """
+73167176531330624919225119674426574742355349194934
+96983520312774506326239578318016984801869478851843
+85861560789112949495459501737958331952853208805511
+12540698747158523863050715693290963295227443043557
+66896648950445244523161731856403098711121722383113
+62229893423380308135336276614282806444486645238749
+30358907296290491560440772390713810515859307960866
+70172427121883998797908792274921901699720888093776
+65727333001053367881220235421809751254540594752243
+52584907711670556013604839586446706324415722155397
+53697817977846174064955149290862569321978468622482
+83972241375657056057490261407972968652414535100474
+82166370484403199890008895243450658541227588666881
+16427171479924442928230863465674813919123162824586
+17866458359124566529476545682848912883142607690042
+24219022671055626321111109370544217506941658960408
+07198403850962455444362981230987879927244284909188
+84580156166097919133875499200524063689912560717606
+05886116467109405077541002256983155200055935729725
+71636269561882670428252483600823257530420752963450
+"""
+
+roll = []
+rollt = 0
+
+best = []
+bestt = 0
+
+for d in num:
+	if not d.isdigit():
+		continue
+	
+	n = int(d)
+	if n == 0:
+		roll = []
+		rollt = 0
+		continue
+	
+	roll.append(n)
+	if len(roll) > 5:
+		rollt -= roll.pop(0)
+	rollt += n
+	if rollt > bestt:
+		best = []
+		for c in roll:
+			best.append(c)
+		bestt = rollt
+
+print best
+m = 1
+for d in best:
+	m *= d
+print m
+
diff -r 000000000000 -r 1ca695e32f66 problem9.py
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/problem9.py	Mon Dec 01 10:57:01 2008 +0000
@@ -0,0 +1,9 @@
+for a in range(1, 1000):
+	for b in range(a + 1, 1000):
+		if a + b > 1000:
+			break
+		for c in range(b + 1, 1000):
+			if a + b + c == 1000 and a*a + b*b == c*c:
+				print "%d^2 %d^2 = %d^2" % (a, b, c)
+				print "a*b*c = %d" % (a*b*c)
+