How big is the colony?
As a zoologist, you discover a new colony of animals on an island. It is composed of 3-legged Zios and 7-legged Zepts. They are moving quickly, but you manage to count the number of legs and know that there is more than one of each type of animal. How can you figure out how big the colony is if you counted 52 legs? Click here to jump to the answer.
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If we let there be a Zios and b Zepts, we know that 3a+7b=52.
Let’s look at multiples of 7 that are smaller than 52: 7, 14, 21, 28, 35, 42, 49.
We can exclude 7 because we know that there must be at least 2 of each creature. Looking at each of the other numbers in turn, we can figure out what 3a would have to be:
Only two of those numbers are divisible by 3 (24 and 3) and we can exclude 3 because that would mean that there is only one Zio. Thus, 3a=24 and 7b=28.
So, a=8 and b=4. This means that we have 8 Zios and 4 Zepts for a total colony size of 12.
Let’s check our answer: 8 Zios x 3 legs + 4 Zepts x 7 legs = 52 legs.
Hat Tip: NRICH
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