Challenge Level

**Lisa** and **Alana** from
Sudbourne School, Lambeth used words to explain how they worked out
the next number:

The answer to what is the next number is $163$ because the difference between $3$ and $7$ is $4$ and the next difference (between $7$ and $19$) is $12$ which is $3 \times 4$. The difference after that (between $19$ and $55$) is $36$ which is $12$ (the last difference) times $3$ (the first number, also the number timsed by $4$ to get $12$.) So we just added $108$ to $55$ which equals $163$.

**Sinan
from** IRMAK Primary School,
Istanbul, Turkey says much the same thing with numbers:

**Sarah
from** Annesley College, Adelaide
South Australia explained it a slightly different way:

I figured it out by working out how much the difference is between the four numbers. Then I found that all the numbers between are all factors of three. So, I times each of the between numbers by three. When I got to $55$ times three I got $108$. Then I added $55$ and $108$ and I got $163$. This was the answer I got.

**Shivana from** Henry Park Primary School, Singapore has another way of
writing it:

The answer is $163$: $n \times 3 - 2$ ($n$ being the previous number).

Example $19 \times 3 - 2 = 55$

**Emir
from** IRMAK Primary School,
Istanbul, Turkey worked it out in a similar way.

The following people also explained their thinking quite well:

**Laura
from** St Ives School,
Haslemere.

**Ruyi
from** Annesley College,
Adelaide South Australia

**Alex
from** The Abbey, Woodbridge,
Suffolk

**Jason
from** Priory
School

**Ruth** and **Jessica from** St Lawrence Primary School, Lechlade.

**Jenny,** **Emily, Caroline, Natalie and
Rebecca from The Mount School York**

**Kathryn, Katerina, Nicola and Andrew from
Primary Maths Club, International School of
Toulouse.**

**Leyla, Gizem, Unal, Melis, Huma, Ece, Idil,
Gizem, Alta, Ece, Simin, Eda S, Ece O, Cana, Sinan, Melike, Efsane,
Emre, Ilayda, Baran fromIRMAK Primary School, Istanbul,
Turkey.**

**Thomas and Justin from Tatingstone
School**

**Michael from St Francis Catholic Primary,
Essex**

**Christina from Malborough
Primary**

**And
finally, a short neat explanation from Steven from Burpham Primary
School, Guildford, Surrey:**

I looked at the sequence of numbers
and worked out the differences between each one. These were $4$,
$12$, $36$.

I realised that $3 \times 4 = 12$,
and that $3 \times 12 = 36$, so the next gap would be $3 \times
36$. That is $108$, so the next number is $163$.