Kelly has a pet store. She recently got in a whole litter of puppies and tried to sell them all.
How many puppies were in the litter? (Hint: Kelly didn’t sell any fractions of puppies!)
Scroll down for the answer!
How can Kelly sell half or a third of a puppy? She can’t, and that’s the key to understanding this problem.
Kelly can only sell exactly half of her puppies if she has an even number of puppies. If she has, say five puppies, then half of five is two and a half, which is not a whole number. If she actually sold three puppies, that would be half of her puppies (2.5), plus another half a puppy.
With this in mind, we can tackle the problem. It’s best done backwards.
On the third day, Kelly sold half her puppies plus a half, and was left with one puppy. She must have started the day with an odd number of puppies. We also know that one is a bit less than half the starting number. A guess and check shows that she started the third day with three puppies.
The second day is trickier, but similar. This time, rather than looking for odd numbers of puppies, look for numbers that aren’t divisible by three. A bit of trial and error will find:
1/3 of 5 = 1 2/3
1 2/3 + 1/3 = 2 puppies sold
5 – 2 = 3 puppies left for day three
So she started day two with five puppies.
Finally, day one is relatively simple. The number of puppies must be odd, and slightly more than double five. If we try 11 puppies we find that she sold six, and ended up with five. This works with the other numbers.
To sum up:
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