# The Real Story of the Cat, the Dog and the Rabbit

Have you seen the email that asks you to figure out the combined weight of a Cat, a Dog and a Rabbit?

This is the kind of email I would normally trash immediately. Math isn’t my stong suit. Oh, I could assign each of the animals  a letter: the Cat a ‘C’, the Dog a ‘D’, and the Rabbit an ‘R’. I could even come up with  three equations: R+C=10; R+D=20; C+D=24. But that would be about as far as I would get before I’d insert a ‘Y’, as in why would I even care.

The Car Guy absolutely loved this email, because his mind likes numbers. He solved the question, even found out what each animal weighed individually, then posted it on Facebook. The response from his friends was almost instantaneous. Some got the answer, some said they were too far into Happy Hour to even guess, and one even posted all the ‘if’, ‘then’, ‘thus’ and ‘therefores’. Even my two young grandsons popped up with the answer, using the ‘guess and check’ (conjecture and proof) method of math that they are learning at school, and it took them less than a minute.

That was when I decided I really did care ‘Y’, and I would find the answer too. First though, I had to fill in the back story so that I could relate to the animals. So here it is:

Grandma had a cat, a dog and a rabbit. They all lived happily on a farm on the right bank of a wide river. The rabbit loved to eat in grandma’s garden, the cat was an excellent mouser, and the dog knew that grandma had a seemingly unlimited supply of kibble and bits.

Somehow (and I’m not too sure how it happened) the three animals woke up one morning on the left bank of the river. This is where the potato farmer lived. The three animals quickly realized that potatoes were not their favourite food, and if they didn’t get back to Grandma’s house quickly, they would perish. The river was too wide to swim, but there was a small boat by the shore and it was just big enough to hold the three of them – as long as they didn’t weigh too much.

The potato farmer had a scale to weigh his bags of potatoes. For some reason the animals couldn’t all get on the scale together, and equally puzzling, they couldn’t get on the scale singly. Instead, they got onto the scale in pairs. With the resulting three pieces of data, they figured out their cumulative weight. They were then able to board the boat, and float across the river without any fear of sinking. The End.

Now you know the real story . Can you answer the question – how much do all three animals weigh? Bonus points if you can tell me how the animals ended up on the left bank of the river AND ‘Y’ they had to weigh themselves in pairs.

I’ll post some answers in the comment section. Don’t peek! I’ll give you a hint though. There is more than one way to find the answer!

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## 24 thoughts on “The Real Story of the Cat, the Dog and the Rabbit”

1. 1. The Math Major’s answer:
If C=10-R and C=24-D then (10-R)=(24-D). Thus (D-R=14) and (D+R=20) thus (14+R=20-R) therefore R=3. The rest is simple. (Easy for him to say!)

2. The Car Guy’s answer:
(D+C)-(D+R)=4
Therefore (C-R)=4
(R+C)+(C-R)=14
Therefore C=7
R+C=10
Therefore R=3
D+R=20
Therefore D=17
R+C+D=27

3. My Answer:
(R+C)+(R+D)=30
(R+D)+(C+D)=44
(C+D)+(R+C)=34
Add these three equations together and you get 4R+4D+4C=108.
Divide both sides by 4 and you get 1B+1C+1D=27.

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2. I hate that teachers are TEACHING “guess and check.” That should be a last resort for the happy-hour crowd.

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• Hopefully ‘guess and check’ is just one method they are taught!

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3. Al says:

Math might as well be Sanskrit for all I understand of it. Oh sure, I know the basics (2+2=5), but higher math escapes me. Not to mention the physical challenge of getting a dog, cat and rabbit to agree to get on a scale together. I think I’ll just check the vet records.

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• I know how you feel, Al. My husband and I were in the same Math 31 class together. I memorized formulas, he understood concepts. This difference is as apparent today as it was about 5 minutes after we wrote the final exam!

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4. When I see numbers, I go cross-eyed and run away. Especially when I’m told children figured it out in less than a minute. That’s intimidating. (Except, of course, that I’m really still a child at heart, so maybe …. nah.)

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• I know how you feel. But when I saw how many people in our family did figure it out, I knew I just had to try harder!

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5. What amazes me is these kids today can do math like this but they can’t make change without a calculator!

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• Yes, I’ve come across that too. We live in a strange time.

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6. My answer is total weight 27. R + 3, C + 7, D = 17. This is what I wrote down –
2D+R+C = 44
2D+10 = 44
2D = 34
D = 17, therefore C = 7 and R = 3

I haven’t worked the other one out yet!

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7. Ha! I’m an old math major who always enjoyed figuring out what ‘x’ equalled. I was never any good at math designed for higher purposes, however… : (

I wrote out the first 3 pictures like this:
rabbit + cat = 10
rabbit + dog = 20
cat + dog = 24

If I combine the first two equations, I get this:
rabbit + cat + rabbit + dog = 10 + 20 = 30
Which I can also write this way:
rabbit + rabbit + cat + dog = 30

I know from the third equation that cat + dog = 24, which means:
rabbit + rabbit + 24 = 30
rabbit + rabbit = 6
rabbit = 3

Which allows me to figure out that cat =7, and dog =17, so the answer is…
rabbit + cat + dog = 3 + 7 + 17 = 27
Hey, that was fun! Thanks, Margie– woof! : )

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• I followed you until the rabbit got to be 3. I’ll have to take your word for how you got the cat and dog. Meow, woof…

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8. Like the above animals, I prefer to get on the scale with another person rather than face the number alone.

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• Well, that explains why they got on in pairs. I’d never thought about it that way.

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9. Well that’s the maths solved, but what about the rest of the story? why did the animals wake up on the other bank.? And, more importantly, why couldn’t they all travel together?
The answer is that they weren’t actually on the other bank at all rabbit’s dream and the animals were so loved by Grandma that even while dreaming rabbit knew how lonely she would be if they all left her. 😉

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• A dream story?! Well that makes as much sense as any other!

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10. ok, i tried briefly, because your subsequent post referred me here. i tried to figure it out and then cheated by googling and was amazed at how many people figured it out – and it is logical. i guess i am a good understander, and not so much a mathematician :O. but thanks for getting my grey matter a bit more active than it was planning on being this evening 😀

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• I never thought to google it – so I did. The simplest answer was “By just adding the weight of the first three pics we can get 54 which is twice the sum of their weights. Dividing by 2 , we can get 27.” Goes to show there is more than one way to skin a cat… though we wouldn’t really skin a cat, or a rabbit either…

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11. Wow, you lost me at “Have you seen the email that asks you to figure out the combined weights of a Cat, a Dog and a Rabbit?” Why in the world wouldn’t you put each animal on the scale one at a time and add it up? Or was that lost when my eyes glazed over?

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• That was my thought too, but there are real world solutions and math world solutions!

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