Random Puzzles 

Workings

Hint
There are twelve items in the full sequence.

Answer
Jly.

From the months with their vowels removed. January, February, March, April, May, June, July.

Workings

Hint
Circumference = 2 x Radius x π.

Answer
6.28 metres, a lot less than you might think!

If we call the radius of the Earth R, then the difference between the two circumferences is:

2 x π x (R + 1) - 2 x π x R
   = 2 x π metres
      = 6.28 metres.

Workings

Hint
You can either fix the distance rowed and see what numbers work, or you can fix the number of hours.

Answer
12 miles.

In the morning, rowing at 2 miles per hour, they rowed for 6 hours. In the afternoon, rowing at 4 miles per hour, they rowed for 3 hours.

There are a number of ways of working this out, and here are two of them:

Method 1
If we assume the distance the rowed upstream to be D miles, we know the morning took (D ÷ 2) hours, and the afternoon took (D ÷ 4) hours, with a difference of 3 hours. So:
 D   D
 - – - = 3
 2   4

Multiplying throughout by 4 gives:

 2D – D = 12

So:

 D = 12 miles

They rowed 12 miles upstream.

Method 2
If we assume they rowed for H hours upstream, we know they travelled H x 2 miles in the morning. In the afternoon, they rowed for (H – 3) hours, and travelled (H – 3) x 4 miles. We know these distances are the same, so:

 2H = (H – 3) x 4

Giving:

 2H = 4H – 12

Rearranging gives:

 12 = 2H

So:

 H = 6 hours

They rowed for 6 hours upstream at 2 miles per hour, which is a total of 12 miles.

Workings

Hint
Some might argue that this isn't a puzzle.

Answer
Half way – after which it would be running out!