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On the first day I travelled 60 miles, leaving 60 miles. On day two I travelled 20 miles, leaving 40 miles On day three I travelled 30 miles, leaving 10 miles. Yesterday I travelled 5 miles, leaving 5 miles.
Puzzle 54
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).
Direct Link: www.brainbashers.com?ZUCK
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.
Puzzle 55
Some months have 30 days, some have 31, but how many have 28 days?
[Ref: ZJCL]
Direct Link: www.brainbashers.com?ZJCL
Hint:
Answer: All of them!
Puzzle 56
My BrainBashers electronic world atlas has developed a fault, I did a listing of miles from England to particular countries and here is the result:
America 1,800 miles
New Zealand 2,400 miles
Japan 1,200 miles
Brazil 1,400 miles
Hint: Vowels (AEIOU) and consonants are each worth a different number of miles..
Answer: 2,200 miles.
Vowels are worth 300 miles and consonants are worth 200 miles.
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