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Noah

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2
We had a small number of submissions but they contained some very interesting thoughts.


Rhea from Bablake Junior School sent in the following 

There are lots of different answers for this. NRICH have put up a very open ended question!
Firstly, lets pretend that all the animals that Noah saw were all 4 legged animals. This would mean that Noah saw 3 animals. You do this by dividing 12 by 4, which is 3.
Secondly, lets pretend that all the animals saw were all 2 legged animals. This would mean that Noah saw 6 animals. You find this out by dividing 12 by 2, which is 6.
Thirdly, lets pretend that all the animals were 3 legged animals. You do this by dividing 12 by 3, which is 4.
Fourthly, lets pretend that that half of the animals Noah saw were 2 legged animals, and the other half were 3 legged animals. To find out the half that were 2 legged, you need to find out what half of 12 is, which is 6. You then have to divide 6 by 2, which is 3! 3 of the animals Noah saw where 2 legged animals. Then, you need to find out how many animals were 3
legged. You do this by dividing 6 (half of twelve: 12 divided by 2) by 3, which is 2. 2 of the animals Noah saw were 3 legged animals.
This is all I have got time for, so make sure you come up with some more solutions for NRICH! Hope you understood 4 of my solutions, thank you for reading this! Bye!

She entered a second submission saying:-

Well, I just entered a solution but I forgot to give examples of some animals Noah could have seen.
For a two legged, maybe birds, like: robins, pigeons, blackbirds, finches, blue tits, doves or swans.
For 4 legged: lion, dogs, cats, tiger, hedgehog, fox, wolf and more. These are examples, but there could be a lot more! Read my other solution on how to work on the 4 legged and two legged animals. It will be very helpful, hopefully you will read it and even make a solution your self! Good luck, hope you have fun on NRICH!

Olivia also from  Bablake Junior sent in this solution:-

There are definitely lots of different ways to solve this! Lets start and pretend that all the animals Noah saw were 1 legged animals. In this very easy case, all you need to do is divide 12 by 1, which is of course 12. This means that if all the animals Noah saw were 1 legged animals, there would be 12 of them. I'm sorry about this, but maybe you know some 1 legged animals? Now lets pretend that all the animals Noah saw were 2 legged animals. In
this case, all you need to do is divide 12 by 2, which is 6. If all the animals Noah saw were 2 legged animals, there would be 6 of them. Now lets think what types of animals they might be. Probably birds- robins, blackbirds, pigeons- maybe even humans- there are lots more!
Now lets pretend that all the animals Noah saw were 3 legged animals (I know there might not be 3 legged animals, but lets pretend there is!) Now all you have to do is divide 12 by 3 which is 4. If all the animals Noah saw were 3 legged animals, there would be 4 of them. Now lets think what type of animals they might be. I'm sorry about this, but I don't know any 3 legged animals, maybe you do? Now lets pretend that all the animals Noah saw were 4 legged animals. In this case, all you need to do is divide 12 by 4, which is definitely 3. So,
if all the animals Noah saw were 4 legged animals, there would be 3 of those animals. Different types of 4 legged animals are dogs, cats, hedgehogs, horses, pigs, cows and lots, lots more! Now lets pretend that all the animals Noah saw were 6 legged animals. (I
know these are probably not real, but lets just pretend, okay?) All you have to do now is divide 12 by 6, which is 2. If all the animal Noah saw were 6 legged animals, there would be 2 of them. They are all the basic solutions, but see if you can mix 2 legged animals and 4 legged animals. There are loads of answers but these are the basics. Hope I've helped, thank you for reading this! Hope you have fun on NRICH!

The teacher of Year 1 at Bute House Prep School sent in the following:-

Year 1 had a lot of fun investigating how many animals could have gone into the Ark if Noah had counted 12 legs.  They thought of their own line of inquiry within this problem and so some looked at whether they could have every number of animal from 1-12 with 12 legs, others looked at how many ways they could have groups of animals with the same number of legs making 12, while others investigated how they could best record their findings
systematically.  Here are a few of their discoveries :-) 

Amelia and Olivia found a number of ways of counting 2,3 and 6 animals, although they realised they couldn’t have a rabbit and a fly as this wouldn’t be enough legs


Annabelle and Julia found solutions for 3, 4 and 6 animals. 



Claudia explored which combinations of the same number of legs  would work to add to 12.

  

Beatrix and Mariana decided that a snail had one leg, a bird 2, a horse 4, an insect 6 and a spider 8 and worked from there. They found solutions for 2,3,4,5,6,11 and 12 animals.

  
Sophie realised that if you used snails it was possible to make up lots of animal numbers eg  4 birds and 4 snails = 8 animals with 12 legs. 6 snails and 3 birds would be 9 animals and 12 legs.
The girls thought 1 animal would be impossible!

Thank you all for these very details accounts of your work. maybe some would go further and consider a larger number of legs seen by Noah. What is there would be only two types of animals and the same numbers of each, which Rhea used.