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Three 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).

Hint: A little algebra might help.

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.

Puzzle 70

Using the clues below can you find 8 four letter words.

Once you have placed the words into the correct order you will find that each word is different from the previous word by only one letter.

For example, FARE may be followed by FIRE, etc.

An imperfection
Additional items
Insufficiently heated
A female equine
Hotter than temperate
An article of commerce
The middle of an apple
Insulated electrical wire

Insufficiently heated = cold
Insulated electrical wire = cord
The middle of an apple = core
Additional items = more
A female equine = mare
An article of commerce = ware
An imperfection = wart
Hotter than temperate = warm

Puzzle 71

If it were two hours later, it would be half as long until midnight as it would be if it were an hour later.

What time is it?

[Ref: ZESJ]

Hint: Think about how many hours to midnight 1 hour later and 2 hours later would be.

Answer: 21:00.

If the time was T, then T + 2 is half the minutes to midnight compared with T + 1.

So 1 hour halves the gap.

This can only happen at 10pm and 11pm, which makes the current time 9pm.

Puzzle 72

How does this make sense?

1 was a race horse
2 was 12
111 race
2112

[Ref: ZLXR]

Hint: Try saying the individual digits.

Answer:
One was a race horse,
Two was one too.
One won one race,
Two won one too.

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