Random Puzzles 

Workings

Hint
The cube root of the given number is a good starting point.

Answer
71, 73, 79.

Reasoning
The cube root of 409,457 is around 74.

The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.

Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.

Workings

Hint
Does ONE work, does TWO work? How many E's are there already?

Answer
Twelve.

"Cleverly, there are exactly twelve E's in this sentence."

Workings

Hint
Ellen liked shrimp, but didn't like eels.

Answer
No.

None of them liked food that started with the same letter as their name.

Workings

Hint
How many clock minutes pass in a real hour?

Answer
1:20pm.

Reasoning
The clock now shows 10:12am, so we know that 10 x 60 + 12 = 612 clock minutes have passed.

Since the clock is losing 6 minutes every hour, for every real hour that has passed, the clock will show 54 minutes.

So, 612 ÷ 54 ≈ 11.33 real hours have passed.

This equals 680 minutes, which is 11 hours and 20 minutes = 11:20am.

The clock stopped 2 hours ago, therefore the time must now be 1:20pm.