Count the routes to a sum

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</style></head><body class="dice"><main><header><p class="kicker">TWO DISTINGUISHABLE DICE / MODEL AND TRIALS</p><h1>Count the routes to a sum</h1><p>Theoretical model: fair, independent six-sided D1 and D2. Thirty-six ordered pairs, not eleven equally likely sums.</p></header><div class="content"><label for="prediction">Before counting: which is more likely, 8 or 3? Why?<textarea id="prediction" rows="3"></textarea></label><div class="controls"><button type="button" id="sum8">Highlight sum 8</button><button type="button" id="sum3">Highlight sum 3</button></div><div class="result" id="theory" aria-live="polite">Ready for an attempt.</div><div class="board" id="pair-grid" aria-label="Ordered pair grid; D1 rows 1 to 6, D2 columns 1 to 6"></div><section class="panel "><h2>Fictional worked sample</h2><p>F1 (2,6) → 8; F2 (1,2) → 3; F3 (4,4) → 8; F4 (6,1) → 7.</p><p>Sample: sum 8 = 2/4; sum 3 = 1/4. The final 7 remains in the denominator. These are not actual rolls or simulation output.</p></section><section class="panel "><h2>Separate manual trial log</h2><div class="fields"><label for="d1">D1 face, whole 1–6<input id="d1" type="number" value="" min="1" max="6" step="1"></label><label for="d2">D2 face, whole 1–6<input id="d2" type="number" value="" min="1" max="6" step="1"></label></div><button type="button" id="add">Add entered trial</button><div class="result" id="entry" aria-live="polite">No trial entered.</div><div class="result" id="frequency" aria-live="polite">Ready for an attempt.</div><div id="trials" class="rows"></div><button type="button" id="reset">Reset experiment</button></section><details id="teacher"><summary>Teacher explanation</summary><p>Five ordered pairs make 8 and two make 3. The theoretical denominator is 36; a trial frequency denominator is the number of recorded trials. A small sample does not revise the model or validate physical dice fairness.</p></details></div><footer><p>Original fictional teaching example. Entries are temporary and are cleared on reload; no responses are sent or saved.</p></footer></main><script>
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