<div data-node-type="callout">
<div data-node-type="callout-emoji">💡</div>
<div data-node-type="callout-text"><strong>Given 11 identical coins but there's a fake coin which has different weight to the others, identify it with 3 trials. </strong><em>Try the simulation game </em><a target="_blank" href="https://fake-coin-puzzle.skyglab.tech/"><strong><em>here</em></strong></a></div>
</div>

<h3 id="heading-demo">Demo</h3>
<iframe src="https://quangnle.github.io/find_the_fake_coin/" width="800px" height="580px"></iframe>

<h3 id="heading-solution">Solution</h3>
<ul>
<li><p>To be convenience for explanation, we number all 11 coins from 1 to 11.</p>
</li>
<li><p>1,2,3 = 4,5,6 (1,2,3,4,5,6 are real):</p>
<ul>
<li><p>1,2,3 =7,8,9 (7,8,9 are real)</p>
<ul>
<li><p>1 = 10 (10 is real) =&gt; 11 fake</p>
</li>
<li><p>1 &lt;&gt; 10 =&gt; 10 fake</p>
</li>
</ul>
</li>
<li><p>1,2,3 &gt; 7,8,9 (either 7,8,9 is fake, lighter)</p>
<ul>
<li><p>7 = 8 (8 is real) =&gt; 9 fake</p>
</li>
<li><p>7 &gt; 8 =&gt; 8 fake</p>
</li>
<li><p>7 &lt; 8 =&gt; 7 fake</p>
</li>
</ul>
</li>
<li><p>1,2,3 &lt; 7,8,9 (either 7,8,9 is fake, heavier)</p>
<ul>
<li><p>7 = 8 (8 is real) =&gt; 9 fake</p>
</li>
<li><p>7 &gt; 8 =&gt; 8 fake</p>
</li>
<li><p>7 &lt; 8 =&gt; 7 fake</p>
</li>
</ul>
</li>
</ul>
</li>
<li><p>1,2,3 &lt; 4,5,6 (7,8,9,10,11 are real)</p>
<ul>
<li><p>1,2,3 = 7,8,9 (either 4,5,6 is fake, heavier)</p>
<ul>
<li><p>4 = 5 (4,5 are real) =&gt; 6 fake</p>
</li>
<li><p>4 &lt; 5 =&gt; 5 fake</p>
</li>
<li><p>4 &gt; 5 =&gt; 4 fake</p>
</li>
</ul>
</li>
<li><p>1,2,3 &lt; 7,8,9 (either 1,2,3 is fake, lighter)</p>
<ul>
<li><p>1 = 2 (1,2 are real) =&gt; 3 fake</p>
</li>
<li><p>1 &lt; 2 =&gt; 1 fake</p>
</li>
<li><p>1 &gt; 2 =&gt; 2 fake</p>
</li>
</ul>
</li>
</ul>
</li>
</ul>
<p><em>The case</em> <strong><em>1,2,3 &gt; 4,5,6</em></strong> <em>is similar to the</em> <strong><em>1,2,3 &lt; 4,5,6</em></strong> <em>case</em></p>
<div data-node-type="callout">
<div data-node-type="callout-emoji">💡</div>
<div data-node-type="callout-text">Try the simulation game <a target="_blank" href="https://fake-coin-puzzle.skyglab.tech/">here</a></div>
</div>

<div data-node-type="callout">
<div data-node-type="callout-emoji">💡</div>
<div data-node-type="callout-text"><strong>Given 11 identical coins but there's a fake coin which has different weight to the others, identify it with 3 trials. </strong><em>Try the simulation game </em><a target="_blank" rel="noopener noreferrer nofollow" href="https://fake-coin-puzzle.skyglab.tech/" style="pointer-events: none"><strong><em>here</em></strong></a></div>
</div>

### Demo

<iframe src="https://quangnle.github.io/find_the_fake_coin/" width="800px" height="580px"></iframe>

### Solution

* To be convenience for explanation, we number all 11 coins from 1 to 11.
    
* 1,2,3 = 4,5,6 (1,2,3,4,5,6 are real):
    
    * 1,2,3 =7,8,9 (7,8,9 are real)
        
        * 1 = 10 (10 is real) =&gt; 11 fake
            
        * 1 &lt;&gt; 10 =&gt; 10 fake
            
    * 1,2,3 &gt; 7,8,9 (either 7,8,9 is fake, lighter)
        
        * 7 = 8 (8 is real) =&gt; 9 fake
            
        * 7 &gt; 8 =&gt; 8 fake
            
        * 7 &lt; 8 =&gt; 7 fake
            
    * 1,2,3 &lt; 7,8,9 (either 7,8,9 is fake, heavier)
        
        * 7 = 8 (8 is real) =&gt; 9 fake
            
        * 7 &gt; 8 =&gt; 8 fake
            
        * 7 &lt; 8 =&gt; 7 fake
            
* 1,2,3 &lt; 4,5,6 (7,8,9,10,11 are real)
    
    * 1,2,3 = 7,8,9 (either 4,5,6 is fake, heavier)
        
        * 4 = 5 (4,5 are real) =&gt; 6 fake
            
        * 4 &lt; 5 =&gt; 5 fake
            
        * 4 &gt; 5 =&gt; 4 fake
            
    * 1,2,3 &lt; 7,8,9 (either 1,2,3 is fake, lighter)
        
        * 1 = 2 (1,2 are real) =&gt; 3 fake
            
        * 1 &lt; 2 =&gt; 1 fake
            
        * 1 &gt; 2 =&gt; 2 fake
            

*The case* ***1,2,3 &gt; 4,5,6*** *is similar to the* ***1,2,3 &lt; 4,5,6*** *case*

<div data-node-type="callout">
<div data-node-type="callout-emoji">💡</div>
<div data-node-type="callout-text">Try the simulation game <a target="_blank" rel="noopener noreferrer nofollow" href="https://fake-coin-puzzle.skyglab.tech/" style="pointer-events: none">here</a></div>
</div>

Find the fake coin puzzle

...interesting things by short notes and demos. Most of notes are in Vietnamese since too few of resources of the language and machine translation EN-VN are not good enough :)
