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f27ad080-9923-48c5-9355-54e4934a95d8.html
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<h4> Activity </h4>
<br>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe scrolling="no" src="https://www.geogebra.org/material/iframe/id/nB8CUK3Y/width/678/height/483/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/false/ctl/false" title="F5.L.A1 Towering Sequence (Hanoi)"> </iframe></div>
</div><br>
<p>In the Tower of Hanoi puzzle, a set of discs sits on a peg, while there are 2 other empty pegs.</p>
<p>A move in the Tower of Hanoi puzzle involves taking a disc and moving it to another peg. There are two rules:</p>
<ul>
<li> Only move 1 disc at a time. </li>
<li> Never put a larger disc on top of a smaller one. </li>
</ul>
<p>You complete the puzzle by building the complete tower on a different peg from the starting peg.</p>
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="eae1b4bc-b7ab-4595-9931-ee48a4b0e593" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>What is the smallest number of moves in which you are able to complete the puzzle with 3 discs?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>7 moves</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b0892daa-0f7a-45e8-931c-98f52a405e3b" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>What is the smallest number of moves in which you are able to complete the puzzle with 4 discs?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>15 moves</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="3d1c2d71-43a6-4082-95a3-a9c5f06d36a1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Jada says she used the solution for 3 discs to help her solve the puzzle for 4 discs. Describe how this might happen.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Jada moved the tower of discs 1–3, then moved disc 4, and then moved the remaining discs 1–3 onto it.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="704b7a8f-b497-4815-8fcc-8fad01a83d04" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>How many moves do you think it will take to complete a puzzle with 5 discs? Explain.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>31 moves. For example: Double the previous answer, and then add 1. The number of moves is 31 because \(2\cdot15+1=31\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8aea9c6a-3f2a-462f-a688-56eb924d07e3" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="5">
<li>How many moves do you think it will take to complete a puzzle with 7 discs? </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>127 moves</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>In this activity, you have started to find a <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">sequence</span> of <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">terms</span>.</p>
<p>Write these definitions in your math notebook.</p>
<ul>
<li>A sequence is a list of numbers, possibly going on forever, such as all the odd positive integers arranged in order: 1, 3, 5, 7, . . . .</li>
<li>The term (of a sequence) is one of the numbers in a sequence.</li>
</ul>