Random Puzzles 

Workings

Hint
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
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

Answer
From the highest floor to lowest we have:
West    Centre  East
====    ======  ====
Harold  Derek   Eddie
Bret    Fred    Greg
Alex    John    Chris

Workings

Hint
Adding the speeds won't work.

Answer
205 mph.

Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.

The first ²/₅ are covered at 123 mph. Therefore, the time taken was [(²/₅) x L] ÷ 123 hours.

The next ²/₅ are covered at 164 mph. Therefore, the time taken was [(²/₅) x L] ÷ 164 hours.

The last ¹/₅ is covered at y mph. Therefore, the time taken was [(¹/₅) x L] ÷ y hours.

The entire trip is covered at an average of 150 mph, and we can conclude that:
 2L      2L      L     L
————— + ————— + ——— = ———
5x123   5x164    5y   150

Rearranging and simplifying gives:
 1     1    2     2
——— = —— - ——— - ———
 y    30   123   164

That means that y = 1 ÷ (¹/₃₀ - ²/₁₂₃ - ²/₁₆₄)

Using a calculator gives y = 205.