You can save the following code as a hypertext file e.g. cooldice.htm and run it by clicking on the file-name. It demonstrates a method that works and a method that fails. Also Gwnn's solution. You can easily include your own.
<!DOCTYPE html>
<html>
<head>
<title>dice</title>
<meta name="author" content="2016 Nigel Guthrie">
<meta charset="utf-8">
<style>
nav {
background: yellow;
position: fixed;
right: 0;
top: 0;
width: 15em;
z-index: 1;
}/* Right menu sidebar */
.D {
text-align: right;
border: medium solid black;
}
.D0, .D1, .D2 {
background: red;
color: white;
font-weight: bold;
text-align: center;
}
.D0 {background: green;}
.D2 {background: blue;}
</style>
</head>
<body>
<nav>
<p>Numberphile 3 dice ==> 2.
<br>Click a transform method</p>
<ul>
<li><a href="javascript: DEMO.show (modmod);">modmod: Modulo 6 and 3.</a>
<li><a href="javascript: DEMO.show (tetris);">tetris: Tetra/tri nums.</a>
<li><a href="javascript: DEMO.show (bigwee);">bigwee: Big and small.</a>
</ul>
</nav>
<script>
const SIDES = 6;
var DEMO = {
a: SIDES,
b: SIDES,
c: SIDES,
start: function start () {
DEMO.a = DEMO.b = DEMO.c = 6
},// initialize demo.
die: function die () {
return 1 + Math.floor (SIDES * Math.random())
},// Random die throw.
rand3: function rand3 () {
return [DEMO.die(), DEMO.die(), DEMO.die()]
},// Random throw of 3 dice.
perm3: function perm3 () {
if (++DEMO.c > SIDES) {
DEMO.c = 1;
if (++DEMO.b > SIDES) {
DEMO.b = 1;
if (++DEMO.a > SIDES) {
DEMO.a = 1;
}
}
}
return [DEMO.a, DEMO.b, DEMO.c];
},// Next higher permutation of 3 dice.
sumMod: function sumMod(d, m) {
return (d[0] + d[1] + d[2]) % m
},// Sum of dice modulo 3.
tri: function tri (n){
return n * (n + 1) / 2
},// Triangular number.
tet: function tet (n){
return n * (n + 1) * (n + 2) / 6
},// Tetrahedral number.
show: function show (dice3) {
h2 = document.createElement ("h2");
document.body.appendChild (h2);
h2.innerHTML = ("Demo of method: " + dice3.name);
DEMO.simulate (DEMO.perm3, dice3, 216);
DEMO.simulate (DEMO.rand3, dice3, 3600);
},// Create table, demonstrate method with permed and random throws.
simulate: function simulate (dice3, transform, chucks) {
var m = DEMO.table (dice3.name);
for (var i = 0; i < chucks; i++) {
var d3 = dice3 ();
var d = transform (d3);
m [d[0]][d[1]].innerHTML++;
m [d[0]][SIDES + 1].innerHTML++;
m [SIDES + 1][d[1]].innerHTML++;
m [SIDES + 1][SIDES + 1].innerHTML++;
// alert ("3 dice: " + d3 + " ==> 2 dice: " + d);
}
},// Count occurences of each pair of dice.
table: function table (text) {
var m = [];
var tb = document.createElement ("table")
document.body.appendChild (tb);
for (var r = 0; r < SIDES + 2; r++) {
var tr = document.createElement ("tr");
tb.appendChild (tr);
m [r] = [];
for (var c = 0; c < SIDES + 2; c++) {
var td = document.createElement ("td");
td.className = "D";
tr.appendChild (td);
m [r] [c] = td;
}
m [r][0].innerHTML = m [0][r].innerHTML = r;
m [r][0].className = "D1";
m [0][r].className = "D2";
}
m [0][0].innerHTML= text;
m [0][0].className= "D0";
m [0][SIDES + 1].innerHTML= m [SIDES + 1][0].innerHTML= "Total";
return m;
},
};// Demo object containing common functions.
function modmod (d) {
/** Promising but failing effort.
Sum mod 3 is the index of the 2nd die.
**/
return [ 1 + DEMO.sumMod (d, 6), d.sort () [DEMO.sumMod (d, 3)]];
};// 3 dice => 2. Choose a die depending on sum mod 3 (fails).
function num35 (a, b, c){
if ((a == b) && (b == c)) return 0;
if (b == c) b = a;
return DEMO.tet (5 - a) + DEMO.tri (5 - b) + 5 - c + 2;
};// Jan van Lent: 3 dice ==> number from 0 to 35 (uniformly).
function tetris (d) {
/** Jan van Lent's solution.
Reduce 3 dice to a number from 0 to 35.
The two dice are n mod 6 and the floor of n/6.
**/
d.sort ();
var n = num35 (d [0], d [1], d [2]);
return [1 + Math.floor (n/6), 1 + n % 6]
};
function bigwee (d) {
/** Gwnn's solution.
Define s as 1, 2, 3, or 4 and B as 5 or 6.
identical numbers: 66
BBB: 55 (nb: just 556 or 566 as 555 and 666 are already taken)
ssB: ss (i.e., forget about the 5 or 6)
sBB: s5 (i.e., take the small one and include a 5)
sss: m6, where m is the sum of the three mod 5.
**/
d.sort ();
if ((d[0] == d[1]) && (d [1] == d[2])) return [6, 6];
if ((d[0] > 4) && (d[1] > 4) && (d[2] > 4)) return [5, 5];
if ((d[0] < 5) && (d[1] < 5) && (d[2] > 4)) return [d[0], d[1]];
if ((d[0] < 5) && (d[1] > 4) && (d[2] > 4)) return [d[0],5];
return [1 + DEMO.sumMod (d, 5), 6];
}
</script>
</body>
</html>
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