Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Have You Got It?

Can you explain the strategy for winning this game with any target?

Counting Factors

Is there an efficient way to work out how many factors a large number has?

Reverse Ages

Age 11 to 14 ShortChallenge Level

Working it out by thinking about the numbers

If Brian's age begins with 1, his father's age should end with 1

Brian's father's age won't end with 1 until Brian is more than 20

If Brian's age begins with 2, his father's age should end with 2

Adding the same number of years to each age

So their ages will be each other's reverses in 11, 22, 33... years time.

Next time is in 11 years, 14 + 11 = 25

Using algebra to find numbers that are each other's reverses and are the correct distance apart
Brian's age written $ab$, Brian's age is $10a+b$
Father's age written $ba$, Father's age is $10b+a$.

$41-14 = 27$ so Brian's father is $27$ years older than Brian.

\begin{align}10a+b+27&=10b+a\\ 10a+27&=10b+a-b\\ 10a-a+27&=10b-b\\ 9a+27&=9b\\ a+3&=b\end{align}
$a$              $b$     Brian's age Father's age
1 4 14 41
2 5 25 52
3 6 36 63
etc.

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