Halloween investigation
Problem
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks.
"We could make costumes up for 
"I could wear a black cloak, green mask and pointy hat", said Ana.
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"Look at me in the black cloak and Dracula mask. Put the crown on me please", said Ross. | Image
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How many possible costumes could Ross have made if he kept the black cloak and Dracula mask but wore one of the different hats?
Here are two other costumes that Ana and Ross made up.
List or draw all of the different cloaks and gowns, masks and hats that they have used.
If they changed around their clothes, hats and masks, how many different costumes do you think Ana and Ross could make?
Find out if your guess was correct.
| Ross found extra masks in the trunk. | Image
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"I think I'll change my face!" laughed Ana. |
I wonder how many other costumes Ana and Ross could put together if they put one of these other masks on.
Can you find out?
| Ana looked deep into the trunk. "I've found a different cape",
she cried. "Now we can make even more costumes!"
How many different |
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How can you be sure that you have found all of the possible costumes?
I wonder how many more different costumes they could possibly make if they had found this bag of old shoes....
Student Solutions
Ali worked hard at this problem and sent us a spreadsheet of the solution. Ali says:
The way we solved the problem is as follows:
1) First, we put all the data into a table.
2) We worked out the combinations for each possibility, then we started to see patterns forming in our solutions table. For example, we saw that in the "masks" column, there is an alternating pattern of "green" and "Dracula".
3) Then, we recognised the same logic in the "Hats" column and the "Cloak" column. There is no variation in the "Gown" column since there is only one type of gown.
4) The answer to the first question is $24$ combinations.
If we look at Ali's spreadsheet, we can see that there are $24$ combinations using:
a black cloak or a wizard's cloak
the grey gown
six different hats (what Ali has called pointy, wizard, crown, Santa, school and muslim)
a green mask or a Dracula mask
5) We used the same method for the next question (using the two new masks, what Ali has called 'old' and 'clown'), but in the spreadsheet we used red to distinguish this part of the question from the others.
6) The answer to the second question is another $24$ combinations, making the total of $48$ combinations.
7) We used the same method for the third question, using yellow to denote the new information on the yellow cloak, as well as the combinations found using this new information.
8) The answer to the third question is another $24$ combinations, making the total of $72$ combinations.
9) For the last part (with addition of the shoes), we added the new information in green in our table.
10) Then we worked through the combinations as before, noticing the repeating patterns.
11) The answer to the fourth question is a grand total of $360$ combinations.
Wow - you have worked very systematically, Ali - well done!