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What is the greatest number of squares you can make by overlapping three squares?

Two Dice

Find all the numbers that can be made by adding the dots on two dice.

Biscuit Decorations

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Butterfly Flowers

Age 5 to 7 Challenge Level:

We had these solutions sent in to this task, which are worth looking at carefully.

Mishika from Bal Bharati Public School, India sent in the following:

First I have joined flowers with the butterflies.
I have added 10 with 5 to make 15
Then added 10 with 6 to make 16
Then added 10 with 2 to make 12
Then added 10 with 9 to make 19
Then added 10 with 4 to make 14
Then added 10 with 1 to make 11
Last I added 10 with 7 to make 17
But I found that there is no pair for the flower 18.

Anvi from James Allen's Prep School wrote:

There are 8 flowers, all numbered between 10 and 20.
There are 16 butterflies, 8 of which are numbered 10.
First I ordered all pairs, each having a number 10 butterfly.
Next, I added the pair.
I then placed the sum of each pair on the corresponding flower.
There was no flower with number 13, hence butterflies 10 and 3 cannot go in any flower.
No pair added to 18, so there can be no butterflies on flower 18.

Macy-May from All Saints C of E Primary School 

So I made all the numbers up but not 18 because there was no 8 and there was only 3 left over:
The only flower that did not have a butterfly was 18.

From the Burke Ward Public School in Australia we had the following:

Students worked in small groups for this investigation.  Initially, each group noticed something different which they shared with the whole class:
- the flowers were different colours (two flowers have the same colour and they followed each other in a counting sequence)
- each flower had a two-digit number (11-19)
- nine flowers
- each of the numbers on the flowers had a 1 in the tens column (eg. 13 is 1 ten and 3 more)

After listening to what each group had noticed students started investigating which butterflies could go together to equal a total on a flower. Groups discovered they needed a butterfly with 10 on it beside each flower (for the value of the 1 in the tens position) and a one-digit butterfly that
added to it to make the total of the flower (e.g.10+3=13).
They changed the tasks slightly and produced this result:

  (Clicking on the image will open a larger version in a new page.)

Thank you for these.