Hard Math Problems That Went Viral in 2018 - Free Printable

We are told:

- Total dogs signed up = 49
- There are 36 more small dogs than large dogs

Let’s define:

- Let L = number of large dogs
- Then, number of small dogs = L + 36

Since the total number of dogs is 49, we can write the equation:

> L + (L + 36) = 49

Simplify:

> 2L + 36 = 49

Subtract 36 from both sides:

> 2L = 13

Divide by 2:

> L = 6.5

Wait — that gives us 6.5 large dogs, which doesn’t make sense in real life — you can’t have half a dog!

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But let’s double-check the problem.

Total dogs: 49
Small dogs = Large dogs + 36

So:

Small + Large = 49
(Small = Large + 36)

Substitute:

(Large + 36) + Large = 49
→ 2×Large + 36 = 49
→ 2×Large = 13
→ Large = 6.5

Still the same.

This suggests there might be an error in the problem setup — or perhaps it’s designed to test if you notice the impossibility.

But maybe we misread?

Let’s try interpreting “36 more small dogs than large dogs” differently? No — that’s standard phrasing.

Alternatively, perhaps the total is wrong? Or the difference?

But assuming the problem is as stated, mathematically:

> Small dogs = L + 36 = 6.5 + 36 = 42.5

Again — not a whole number.

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✔ Conclusion: With the given numbers, there is no integer solution — meaning it’s impossible for there to be 49 total dogs with exactly 36 more small dogs than large dogs, since that would require half a dog.

However, if this is a math problem expecting an answer, perhaps it's a trick question — or maybe there's a typo.

Let’s check: If total were 50 instead of 49:

> 2L + 36 = 50 → 2L = 14 → L = 7 → Small = 43 → Total = 50 ✔

Or if difference were 35:

> 2L + 35 = 49 → 2L = 14 → L = 7 → Small = 42 → Total = 49 ✔

So likely, there’s a typo in the problem.

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But since you asked to solve the problem *as given*, and assuming we must provide an answer:

Mathematically:

Number of small dogs = 42.5

But since dogs must be whole numbers, this situation is impossible.

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💡 Final Answer (with explanation):

> There is no valid whole-number solution to this problem as stated. The math leads to 6.5 large dogs and 42.5 small dogs, which is impossible in reality. This suggests there may be an error in the problem — perhaps the total number of dogs or the difference should be adjusted to allow for whole numbers.

If forced to give a numerical answer based purely on algebra:

> 42.5 small dogs

But realistically, the problem has no valid solution.