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### Number and algebra

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# The Tall Tower

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### Biscuit Decorations

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Age 5 to 7

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These solutions show some interesting ideas, thank you for sending them in.

Gabby from Walthamstow Hall Junior School said:

I thought that to get the highest number of spells in total it would not matter if I didn't go into as many rooms as I could, it would matter that I could get into most of the rooms with higher numbers of spells in it so I could get a higher total. I then tried a couple of solutions to see which route would have the highest total of spells.

Casey from a school in Australia wrote:

You go through room 1 to room 3 then 4 then 6 then 5 then 7 and then 9 that gets you 35 spells.

Which way should you go to collect the most spells?

A solution is room 1 then room 3 then room 4 then room 6 then room 5 then room 7 then room 8 then room 10 then room 9. So then that gets you 53 spells.

Igor from the International School of Luxembourg sent in the following:

On the left side there are all the odd numbers and on the right, there are the even ones. In this example all the even numbers on each floor are bigger than the odd ones so to collect fewer spells you go left and to collect more you go right.

I'm almost 100% sure that there is only one way of doing the puzzle but I don't think I could come up with it.

Jacob from Moulton CEVC Primary School wrote:

To collect exactly 35 spells I started with subtracting the number you have to go through to exit the tower (9) then I worked out how to make 26 with the numbers left.

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?