### What's it Worth?

There are lots of different methods to find out what the shapes are worth - how many can you find?

### Turnips

Baldrick could buy 6 parsnips and 7 turnips, or 8 parsnips and 4 turnips. How many parsnips could he buy?

### To Run or Not to Run?

If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

# Magic 7

##### Age 11 to 14 Short Challenge Level:

7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 99 = sum of all 3 rows
$\therefore$ sum of each row is 33

Writing the numbers in terms of $n$

\begin{align}26-2n\ \ +\ \ 19-n\ \ +\ \ 12\ \ &=33\\ 26+19 + 12-33&=3n\\ 24&=3n\\ 8&=n\end{align}

Writing the numbers in terms of $x$
7 + 14 = 21, 12 is missing to make 33

Say $n$ + 12 + $x$ + 12 = 33,

then $n$ + 14 + ($x-$2) = 33

Same idea gives $x-$4 at the bottom

$\therefore$ 3$x$-6=33, so $x$ = 13

And $n$ + $x$ + 12 = 33 $\Rightarrow n$ + 13 + 12 = 33 $\Rightarrow n$ = 8

Using reasoning and not algebra
7 + 14 = 21, 12 is missing to make 33

33 $-$ 14 = 19
19 = 7 + 12
19 = 8 + 11
19 = 9 + 10
no more options so these 4 numbers are 8, 9, 10, 11

$n$ + middle + 14 = bottom + middle + 12

difference between $n$ and bottom = difference between 12 and 14

This gives 2 options:

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.