Random Puzzles 

Workings

Hint
What are the maximum and minimum tonnes of pig feed I could have bought?

Answer
I bought 15 tonnes of chicken feed, 75 tonnes of pig feed, and 10 tonnes of cattle feed.

 15 x 0.15 =    2.25
 75 x 1.25 =   93.75
 10 x 0.40 =    4.00

100 tonnes = $100.00

A possible solution method follows …

I couldn't have bought 80 tonnes of pig feed because this would have cost the full $100.00, but I wouldn't have then had 100 tonnes in total.

Similarly, 70 tonnes of pig feed would have been too few, as this would cost $87.50 and even the remaining 30 tonnes all being cattle feed wouldn't have reached the required $100.00.

So, let's try 71 tonnes of pig feed = $88.75:

   plus 1 x chicken feed + 28 x cattle feed is over $100.00
   or   2 x chicken feed + 27 x cattle feed is under $100.00

   so 71 tonnes of pig feed doesn't work.

Let's try 72 tonnes … and so on.

We soon get to 75 tonnes of pig feed and find the answer.

Workings

Hint
There are fewer than 1,000 apples.

Answer
946 apples.

Reasoning
We know that (answer − 1) is divisible by 3, 5, 7, and 9.

If it's divisible by 9 then it's automatically divisible by 3.

So the number must be a multiple of 5, 7, and 9.

   [5 x 7 x 9 = 315]

Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+ 1).

Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73, and this doesn't work.

Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36, and this doesn't work.

Let's try 3 x 315 + 1: 946 ÷ 11 = 86, and this works, and is the answer.

Workings

Hints
The first letters of the words are: T, C, C, G, T, B, S, B, D, G.

Answers
----rem = theorem ----oct = concoct ----pso = calypso ----dma = grandma ----edo = torpedo ----rre = bizarre ----sfy = satisfy ----ott = boycott ----hma = drachma ----dpa = grandpa

Workings

Hint
There are 1,760 yards in a mile, 3 feet in a yard, and 12 inches in a foot.

Answer
Inches in a mile.

Reasoning
There are 1,760 yards in a mile, 3 feet in a yard, and 12 inches in a foot.

There are 1760 x 3 x 12 = 63,360 inches in a mile, and around 1,000 x 52 = 52,000 Sundays in a thousand years.

Depending on the day of the week the first day of the year falls, there are either 52,177 or 52,178 Sundays in a thousand years.