[OK]

See Details
Privacy Policy + T&C

We use cookies to personalise content and adverts. We also share information about your use of our site with our advertising partners who may combine it with other information you’ve provided to them or they’ve collected from your use of their services. You also agree to our terms and conditions (T&C).

BB Logo
Spacer
Line
Line

Puzzle - Answer

In farmer Brown's hay loft there are a number of animals, in particular crows, mice and cockroaches.

Being bored one day, I decided to count the animals and found there were exactly 150 feet and 50 heads in total, and there were twice as many cockroaches as mice.

How many of each animal were there?

 [Ref: ZVYU] © Kevin Stone

Answer: 10 cockroaches, 5 mice and 35 birds.

Cockroaches have 6 feet, mice have 4 and birds have 2.

For every mouse there are two cockroaches, so every mouse is worth 3 heads and 16 feet (4 + 6 + 6).

We can now write down an expression for the heads and the feet (calling birds B and mice M):

Heads gives us:
   B +  3M = 50       (1)
Feet gives us:
  2B + 16M = 150      (2)

If we double (1) we get:

  2B +  6M = 100      (3)

We can now do (2) - (3) to give:

        10M = 50
          M = 5
So we have 5 mice (and 10 cockroaches). We can use M = 5 in (1) to give:

  B + 3 x 5 = 50
     B + 15 = 50
          B = 35

So, C = 10, M = 5 and B = 35. Checking that 10 + 5 + 35 = 50, and 10 x 6 + 5 x 4 + 35 x 2 = 150. QED.

Back to the puzzles...


Our Favourite Illusions

 Shadow Illusion

 What Am I?

 Hidden Faces

 Impossible Waterfall?

 Same Eyes?

 Impossible Prongs?

 Duck Or Rabbit?

 Spinning Dancer

 Who Turned To?

 Blind Spot

 The Butterfly

 Parallel Cafe Wall Lines?

 

 



We use cookies to personalise content and adverts. We also share information about your use of our site with our advertising partners who may combine it with other information you’ve provided to them or they’ve collected from your use of their services. For more information please view our privacy policy. By using the site you also agree to our terms and conditions.

Line
Line