## Welcome to the dog show

By Ariel Marcy, 13 July 2023

**Difficulty: Fun**

There are 50 total dogs signed up for a dog show. There are 30 more small dogs than large dogs. How many small dogs have signed up to compete in the show?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

You can’t have negative dogs! If there are always 30 more small dogs than large dogs, what’s the smallest number of small dogs possible? What happens to the total if you add one large dog?

## Brainteaser answer

There are 40 small dogs in the dog show.

If there are 30 more small dogs than large dogs, then the smallest possible number of small dogs is 30 with 0 large dogs, for a total of 30 dogs. Obviously, we need more dogs.

If we add 1 large dog, we also need to add a small dog so the difference is still 30. 31 small dogs plus 1 large dog makes 32 total dogs. Notice how the total goes up 2 for every 1 large dog added.

Starting from the 30-dog baseline, we want the total to go up by 20. Half of that increase needs to be big dogs, and the other half needs to be small dogs.

So we get 30 + 10 = 40 small dogs, and 0 + 10 = 10 big dogs for a total of 40 + 10 = 50 dogs!

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13 July, 2023 at 3:54 pm

Somewhere between 30 and 40 small dogs in the dog show. There’s 40 small dogs in the dog show only if you assume no other size categories of dogs.