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<p> The number $24$ is special because it is just one short of being a square number.</p>
<p> So $24 + 1 = 25$ and $5^2 = 25$</p>
<p> AND when you double $24$ the answer is also one short of being a square<br></br>
number.</p>
<p>So $24 \times 2 = 48$ and $48 + 1 = 49$ and $7^2 = 49$.</p>
<p>Find another number that is special in the same way as $24$.</p>
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<p>This one is tough! <strong style="font-weight: 400;">Susannah</strong> from Headington Junior School
has given it a try...</p>
<p>"The closest I can get is 8 times 8 which is 64, - 1 = 63.</p>
<p>63 + 63 = 126, 121 is 11 squared.</p>
<p>8.5 times 8.5 = 72.25, rounded up to 73.</p>
<p>72 + 72 = 144 which is 12 squared".</p>
<p><strong style="font-weight: 400;">Sara from E</strong>ast
Bergholt VC Primary, Suffolk</p>
<p>"At first I thought it was hard, but in the end it was easy!</p>
<p>840 + 1 = 841<br></br>
841 = 29 x 29</p>
<p>840 x 2 = 1680</p>
<p>1680 + 1 = 1681<br></br>
1681 = 41 x 41</p>
<p>So the Special Number is 840."</p>
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<h3><span style="font-weight: bold;">Why do this
problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=946&part=index">
This problem</a> gives practice in calculating, but it also offers
a good point from which to open up a challenge and allow pupils
freedom to explore (see the ideas below).</div>
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<h3>Key questions</h3>
<div>What number could you try?</div>
<div>Will you need to try a bigger or smaller number next?</div>
<br></br>
<h3>Possible extension</h3>
<div><a href="/content/99/05/penta3/Special24.pdf">This sheet</a>
gives some possible extension ideas.</div>
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Special 24
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Using, Applying and Reasoning about Mathematics
Trial and improvement
Calculations and Numerical Methods
Multiplication & division
Calculations and Numerical Methods
Addition & subtraction
Information and Communications Technology
Calculators
Numbers and the Number System
Square numbers