### Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

### Not a Polite Question

When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

# Grow up Fast

##### Age 11 to 14 ShortChallenge Level

Using the number of years that have passed
 Julie Megan Zoey today 32 4 1 in $n$ years 32 + $n$ 4 + $n$ 1 + $n$

32 + $n$ = 4 + $n$ + 1 + $n$
= 5 + 2$n$
27 = $n$

In 27 years Julie will be 32 + 27 = 59

Using algebra and Julie's age
Julie's age is $J$

$32-4=28$ so Megan's age is $J-28$
$32-1=31$ so Zoey's age is $J-31$
\begin{align}(J-28)+(J-31)&=J\\ \Rightarrow 2J-59&=J\\ \Rightarrow J&=59\end{align} So Julie will be $59$.

Using trial
 Julie Megan Zoey M + Z 32 4 1 42 14 11 25 too small 52 24 21 45 too small 62 34 31 65 too big 61 33 30 63 too big 59 31 28 59 perfect

Julie is 59

You can find more short problems, arranged by curriculum topic, in our short problems collection.