### Buzzy Bee

Buzzy Bee was building a honeycomb. She decided to decorate the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

### Fair Exchange

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

### Domino Number Patterns

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of 3 dominoes?

# The Tall Tower

##### Stage: 1 Challenge Level:

Complete solutions to this problem were sent in by Michael from Beecroft Primary School, Nathalie from Hartley Primary and Hilary who goes to ESF Bauhinia School. In response to the first part, Michael sent us a very clear image to show how to collect the most spells:

He explains his reasoning:

The most number of spells able to be collected is $1+3+4+5+6+7+8+9+10=53$. You don't go through the room with $2$ spells so go straight down the ladder to room $3$, then $4$, then $5$ etc... Since you start in room 1, you have to collect the single spell so the lowest number of spells to miss is two! If you go to room two then you will miss on a bigger lot of spells.

An excellent point, Michael. Hilary wrote:

For the second task we have to find the fewest spells on the path. The answer for the second task was $25$. I simply just go $1, 3, 5, 7, 9$.

Finally, Nathalie found a route that makes a total of exactly $35$ spells:

$1, 3, 4, 6, 5, 7, 9 = 35$

Well done all three of you.