[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

SheepThree countrymen met at a cattle market. "Look here," said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got."

"If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I."

"Well, I'll go better than that," said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six times as many animals as I've got here."

No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge, and Durrant must have taken to the cattle market.

 [Ref: ZUCK] At A Cattle Market. Amusements In Mathematics by Henry Ernest Dudeney (1917).

Answer:
Jakes must have taken 7 animals to market, Hodge must have taken 11, and Durrant must have taken 21. There were thus 39 animals altogether.

This can be solved with a little algebra, where J - Jakes, H = Hodge and D = Durrant:

From the clues:

2 x (H - 6 + 1)  = J + 6 - 1       [1]

3 x (D - 14 + 1) = H + 14 - 1      [2]

6 x (J -4 + 1)   = D + 4 - 1       [3]

These can be rearranged to give:

2H - J = 15                        [4]
3D - H = 52                        [5]
6J - D = 21                        [6]

We can now use 2 x [5] + [4] to give:

6D - J = 119                       [7]

We can now use [7] + 6 x [6] to give:

35J = 245
  J = 7

We can then use J = 7 in [4] and [6] to give H = 11, and D = 21. 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?

 

 



BrainBashers™ is a trademark. 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