Random Puzzles 

Workings

Hint
How much of a warren can each rabbit dig in one hour?

Answer
2 hours.

Reasoning
The small rabbit can dig a warren in nine hours, so digs ¹/₉ in one hour.

The medium rabbit can dig a warren in 6 hours, so digs ¹/₆ in one hour.

The large rabbit can dig a warren in four and a half hours, so digs ¹/_4.5 in one hour.

   1 Hour = ¹/₉ + ¹/₆ + ¹/_4.5

To make the denominators all the same, we can multiply through by ¹⁸/₁₈ to give:

   1 Hour = ²/₁₈ + ³/₁₈ + ⁴/₁₈

   1 Hour = ⁹/₁₈

   1 Hour = ¹/₂

So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.

Workings

Hint
helium = h-- + l--

Answers
helium = hum + lie latest = let + sat almond = man + old eldest = led + set placed = cap + led radium = air + mud desert = red + set wealth = law + the tricky = cry + kit funnel = elf + nun
Alternative Answers
The following answers use less common words.

helium = him + leu
helium = hue + mil
helium = hum + lei

latest = els + tat

almond = don + lam
almond = lam + nod

eldest = eld + set
eldest = els + ted

placed = pec + lad

radium = mud + ria
radium = amu + rid
radium = aid + rum

wealth = awl + the
wealth = haw + let

There are more answers with even rarer words, but I've chosen not to include those.

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
A baker's dozen is 13.

Answer
Hours in a week.

Reasoning
A dozen is usually 12, but a baker's dozen is usually 13.

So a dozen (12) baker's dozen (13) = 12 x 13 = 156.

There are 24 hours in a day, and 7 days in a week.

So there are 24 x 7 hours in a week = 168.