forked from BostonPython/puzzles
-
Notifications
You must be signed in to change notification settings - Fork 0
/
lock.html
81 lines (55 loc) · 3.18 KB
/
lock.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
<!DOCTYPE html>
<html>
<head>
<title>Puzzle: Letter Lock Picking</title>
<link rel="stylesheet" type="text/css" href="style.css">
<body>
<p class="subtle"><a href="/">« Boston Python puzzles</a></p>
<h1>Letter Lock Picking</h1>
<p>[inpsired by <a href="http://www.datagenetics.com/blog/march32012/">http://www.datagenetics.com/blog/march32012/</a>]</p>
<p>Consider a combination lock that uses letters rather than numbers. For
example, the <a href="http://www.amazon.com/Master-Lock-1535DWD-Vertical-Resettable/dp/B009JTW84Y">Masterlock 1535DWD Vertical combination lock</a>:</p>
<p class="display"><img src="lock.jpg" alt="Masterlock word combination lock"/></p>
<p>It has 4 rings with 10 letters each:</p>
<pre>
RINGS = ['BDMJPRSTLN', 'AEIOUYRTLH', 'ACDEORSTLN', 'DHKYRSTLNE']
</pre>
<p>In principle, just like the space of 4-digit base-10 numbers, there are
10,000 possible combinations. But in practice, there are far fewer.</p>
<p>1. How many English words can be made with this lock?</p>
<p>The answer will depend on what dictionary you use. On a Mac, this will get
you English words as a Python list of uppercase strings:</p>
<pre>
words = open('/usr/share/dict/words','r').read().upper().split('\n')
</pre>
<p>Now let's say that you're trying to crack this lock, and here is what you
know about the correct combination:</p>
<ul>
<li>The correct combination is a valid English dictionary word.</li>
<li>The word is also a member of the small set of triple words for this
lock, meaning that all 3 words appear on one configuration of the
rings.</li>
<li>These triple words are a time, a chemical, and a food. (And the correct
combination word is the food.)</li>
</ul>
<p>2. What is the correct combination for this lock?</p>
<p>Bonus question:</p>
<p>3. How many twin words and triplet words are there? What about higher
levels of word multiples?</p>
<p>Open questions:</p>
<p>4. Change the letters of this lock (again with 4 rings with a set of 10
unique letters on each) to find the lock with the most multiple words of the
highest order. How high can we go with English? Quadruplet words? Quintuplets?
Sextuplets? Septuplets... octuplets??</p>
<p>5. And finally, how about siamese twin words, i.e. words that are adjacent
to each other on the rings? What is the highest order of 4-letter siamese twin
words that can be generated in English with 10-letter rings? What if it were a
lock with full 26-letter alphabetic rings? (This last question is really more
of a question about the English language than about combination locks.)</p>
<h2>Solutions</h2>
<ul>
<li>Steve Witham's solution is <a href="http://nbviewer.ipython.org/github/switham/puzzles/blob/gh-pages/solutions/switham/wordlock.ipynb">wordlock.ipynb</a></li>
<li>Chuck Mock's solution finds the food and time to answer # 2: <a href="https://github.com/BostonPython/puzzles/blob/gh-pages/solutions/cmock/wordlock_cm.py">wordlock_cm.py</a></li>
<li>Jon Kiparsk's solution is <a href="https://github.com/BostonPython/puzzles/blob/gh-pages/solutions/kiparsky/letterlocks.py">letterlocks.py</a></li>
</ul>
<p>If you have a solution you'd like to share see the <a href="solutions.html">Solutions page</a> for instructions.</p>