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Starfish Spotting

Age 5 to 7 Challenge Level:
Luis, Mason and Diego from Buckeye Elementary School in Arizona, USA sent in the following 3 solutions:

Children:4 Starfish:4;  Children:9 Starfish:2;  Children:14 Starfish:0;

Children:2 Starfish:1 I did this because some species of starfish have more arms than other species

 


Navdeep from Great Oaks Elementary School in Texas, sent in:

4 starfish = 20 arms; 4 kids = 8 arms; total 28 arms


Daisy and Amelie from Kingswear Primary wrote:

There could be 2 starfish on the beach and 9 children because children have 2 arms, double 9 would be 18. 18 plus the number of arms of 2 starfish which adds up to 10 because starfish have 5 arms, so you add 10 to 18 and you get 28.


Isabel from St Swithun's Prep School wrote about how to go about solving the task:


 

Isabella from York House School in Canada sent in the following:

We first figured out that the number of starfishes' legs have to equal an even number so that each human would have 2 arms. Then we did 5x4=20 and 28-20=8 and 8/2=4. I found other solutions by making a table.

  

Henry from Abbots Ripton sent in the following explanation:


I assumed that all starfish have 5 arms and all the children have 2 arms.
I figured out that you could have no starfish and 14 children.
You can’t have 1 starfish as this leaves an odd number of arms, so you can have 2 starfish as this is 10 arms, and 9 children with 18 arms.
You can’t have 3 starfish because that would leave an odd number of arms.
You can have 4 starfish and 4 children.
You can’t have 5 starfish as the would give you an odd number of arms. 
You can’t have 6 starfish or more because it would be too much.

Lauren and Violet from Westridge School for Girls in Pasadena wrote a good explanation: 


Our answer is 4 sea stars and 4 children. Our strategy is that we subtracted the number of arms by adding more stars and children. We started with number 28 and subtracted by 5s until we got 13. Then we started to subtract starting with 13 by 2s. When we got to 5, we realized that one sea star has 5 arms, so we subtracted the final 5 arms to get 1 more star and we had no arms left. Then we counted a total of 4 stars and 4 children.

Saya and Micaela from the same school said:

First we started with the number of arms, and we figured out that for the starfish we would have to have a multiple of five. So, then we knew that each of the humans would have a multiple of two. Then we took eight away from the 28 and divided the eight by two (for each of the humans). We got four.
Then we used the remaining 20 and divided that by five (for each of the starfish) and we got four. So our final answer comes out four humans and four starfish.

Thank you for these solutions, I just wonder how many different solutions there are for some different totals?