Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

Weekly Problem 50 - 2006

Stage: 2, 3 and 4 Challenge Level:

$a=2$, $f=8$, $l=7$, $w=6$ and $y=5$.

We note first that $y=5$ since that is the only non-zero digit that, when it is multiplied by 3, has itself as the units digit. So there is a carry of 1 into the tens column. We note also that $a=1$ or $a=2$ as "$fly$"$< 1000$ and therefore $3\times$ "$fly$"$< 3000$. We now need $3\times l+1$ to end in either 1 or 2 and the only possibility is $l=7$, giving $a=2$ with a carry of 2 into the hundreds column. As $a=2$, $f$ must be at least 6. However, if $f=6$ then $w=0$ which is not allowed. Also, the letters represent different digits, so $f\neq 7$ and we can also deduce that $f\neq9$ since $f=9$ would make $w=9$. Hence $f=8$, making $w=6$ and the letters represent $875\times 3=2625$.

This problem is taken from the UKMT Mathematical Challenges.

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