Random Puzzles 

Workings

Hint
How many watch minutes pass in a real hour?

Answer
8:10am.

Reasoning
The watch now shows 8:26am, so we know that 8 x 60 + 26 = 506 watch minutes have passed.

Since the watch is gaining 6 minutes every hour, for every real hour that has passed, the watch will show 66 minutes.

So, 506 ÷ 66 ≈ 7.666 real hours have passed.

This equals 460 minutes, which is 7 hours and 40 minutes = 7:40am.

The watch stopped 30 minutes ago, therefore the time must now be 8:10am.

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
You can only go up, or right.

Answer
6.

With U = Up, and R = Right, you can move in the following ways:
UURR
URUR
URRU
RUUR
RURU
RRUU

Workings

Hint
A tricky base 8 question.

Answer
61.

Each term is a square expressed in base eight, 7 2=49 = 61 in base 8.