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<link type="text/css" rel="stylesheet" href="http://pasterack.org/scribble.css"/><link type="text/css" rel="stylesheet" href="http://pasterack.org/racket.css"/><link type="text/css" rel="stylesheet" href="http://fonts.googleapis.com/css?family=Droid+Sans+Mono"/><div style="font-family:'Droid Sans Mono',monospace;background-color:transparent"><ol start="0" style="font-size:70%;color:#A0A0A0"><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><a class="RktModLink" data-pltdoc="x" href="http://docs.racket-lang.org/guide/Module_Syntax.html#%28part._hash-lang%29"><span class="RktMod">#lang</span></a><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><a class="RktModLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/index.html"><span class="RktSym">racket</span></a><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/require.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._require%29%29">require</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">data/enumerate</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">data/enumerate/lib</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29">define</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">num-dice</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">8</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/define.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._define%29%29">define</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">num-sides</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">6</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/define.html#%28form._%28%28quote._~23~25kernel%29._define-values%29%29">define-values</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym">total-ways</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">ways-with-all-values</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/for.html#%28form._%28%28lib._racket%2Fprivate%2Fbase..rkt%29._for%2Ffold%29%29">for/fold</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">total-ways</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">]</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">[</span><span class="RktSym">ways-with-all-values</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym">dice</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/data/Enumerations.html#%28def._%28%28lib._data%2Fenumerate..rkt%29._in-enum%29%29">in-enum</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/data/Enumerations.html#%28def._%28%28lib._data%2Fenumerate%2Flib..rkt%29._listof-n%2Fe%29%29">listof-n/e</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/data/Enumerations.html#%28def._%28%28lib._data%2Fenumerate..rkt%29._below%2Fe%29%29">below/e</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">num-sides</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">num-dice</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/values.html#%28def._%28%28quote._~23~25kernel%29._values%29%29">values</a></span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._add1%29%29">add1</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">total-ways</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2B%29%29">+</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">ways-with-all-values</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktStxLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/if.html#%28form._%28%28quote._~23~25kernel%29._if%29%29">if</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._~3d%29%29">=</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/sets.html#%28def._%28%28lib._racket%2Fset..rkt%29._set-count%29%29">set-count</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/sets.html#%28def._%28%28lib._racket%2Fset..rkt%29._list-~3eset%29%29">list->set</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">dice</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">num-sides</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">1</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">0</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"> </span></span></li><li><span style="font-family:'Droid Sans Mono',monospace;font-size:125%"><span class="RktMeta"></span><span class="RktPn">(</span><span class="RktSym"><a class="RktValLink" data-pltdoc="x" href="http://docs.racket-lang.org/reference/generic-numbers.html#%28def._%28%28quote._~23~25kernel%29._%2F%29%29">/</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">ways-with-all-values</span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktSym">total-ways</span><span class="RktPn">)</span><span class="RktMeta"></span></span></li></ol><p>=></p><blockquote><table style="font-size:90%;table-layout:fixed;width:100%;word-wrap:break-word"><tr><td><p><span class="RktRes">665/5832</span></p></td></tr></table></blockquote></div>
dice
#lang
racket
(
require
data/enumerate
data/enumerate/lib
)
(
define
num-dice
8
)
(
define
num-sides
6
)
(
define-values
(
total-ways
ways-with-all-values
)
(
for/fold
(
[
total-ways
0
]
[
ways-with-all-values
0
]
)
(
[
dice
(
in-enum
(
listof-n/e
(
below/e
num-sides
)
num-dice
)
)
]
)
(
values
(
add1
total-ways
)
(
+
ways-with-all-values
(
if
(
=
(
set-count
(
list->set
dice
)
)
num-sides
)
1
0
)
)
)
)
)
(
/
ways-with-all-values
total-ways
)
=>
665/5832