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Heads and Feet

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2
We had a few good solutions sent in and here we see a selection with some information about how the answer was achieved. First from St. Mary's School Maths Club in Wales:

We started by drawing 8 heads. Then we gave each head 2 legs. This gave us a total of 16 legs.
We calculated 22-16 and were left with 6.
We knew we had to split the remaining legs into 2's (so we could add to the 2 we had already and make 4)
So 6 divided by 2 was 3.
We gave 3 heads 2 more legs and in the end we had 4 hens and 3 sheep.
We checked it by saying 4 x 2 = 8 and 3 x 4 = 12
8 + 12 = 22!
We enjoyed this problem and liked using our brains!

Then Riziki, who is home schooled in South Africa, sent this:

First I tried to make 8 in different ways using cuisinaire rods of 2 and 4: (the S represents the sheep and the H, the hens) 1S +7H, 2S+6H, 3S+5H, etc
Then in each case I added up the total number of legs e.g: 1S + 7H = 4+ (7 of 2 or 7 x 2) legs = 18 legs and the correct answer was 5 hens and 3 sheep. This was the only possible answer.

Summer at Valence Primary School sent in the following:

I did trial and error to solve this problem:
         Sheep feet:    hen feet:    heads:    total feet
         ________________________________________________
             4             :       2          :      2     :         6
             8             :       4          :      4     :         12
             12           :       6          :      6     :         18
            
The next line can't be one more sheep and one more hen or else there would be 24 feet instead of 22 feet, and there HAS to be two more heads/animals, so it ends up with two more hens.

Evie at Highview Primary School wrote:

I started with 8 hens to see if it was right but there weren't enough legs.
Next I took away a hen and added a sheep but there still weren't enough legs.
I kept taking away hens and adding sheep until I got to the right answer.
5 x 2 = 10 (5 hens with 2 legs each)  3 x 4 = 12 (3 sheep with 4 legs each) 10 + 12 = 22

Miss Owen, the year 2 teacher at The Edmunds Primary School wrote:

Today we worked on this problem using trial and error. First we all worked on the possibility that there were 4 hens and 4 sheep however found that there were too many legs. So we worked with our partners to try other combinations of numbers that added up to 8 (3 hens 5 sheep etc) until Matthew and Billy worked out that the answer was 5 hens and 3 sheep. 3 sheep have 12 feet, 5 hens have 10 feet so altogether 8 heads, 22 feet.

Thank you for all your contributions, it would seem you really enjoyed this challenge.