Random Puzzles 

Workings

Hint
How many minutes are there between 2:00 and 7:00?

Answer
65 minutes.

Reasoning



We need to break down the five hours in the following way:

3 x Answer minutes past two o'clock 40 minutes Answer minutes before seven o'clock
Why? It is now Answer minutes before seven o'clock, and then we have the 40 minutes before that, and the remaining time was 3 x Answer minutes past two o'clock.

So, five hours = 5 x 60 = 300 minutes. We already know about the 40 minutes, so we have to share the remaining 260 minutes in the ratio 3:1, which gives 195:65 minutes. Or using algebra 4 x Answer = 300 − 40, so Answer = 65 minutes.

Therefore, the five hours is made up of:

195 minutes past two o'clock 40 minutes 65 minutes before seven o'clock
So, it's currently 65 minutes before 7:00 = 5:55.

Double-Checking
It is now 65 minutes before seven o'clock = 5:55, so 40 minutes ago it was 5:15 – which is 195 minutes after 2:00, as required (as 65 x 3 = 195).

Workings

Hint
How many pieces on the top layer had two sides with icing?

Answer
15 pieces.

Reasoning
On each layer there are 4 pieces with exactly two sides of icing.

Therefore Kevin ate 12 pieces, leaving 15 for the guests.

Workings

Hint
There are fewer than 1,000 apples.

Answer
946 apples.

Reasoning
We know that (answer − 1) is divisible by 3, 5, 7, and 9.

If it's divisible by 9 then it's automatically divisible by 3.

So the number must be a multiple of 5, 7, and 9.

   [5 x 7 x 9 = 315]

Since these numbers share no other common factors, we know that the answer must be a multiple of 315 (+ 1).

Let's try 1 x 315 + 1: 316 ÷ 11 = 28.73, and this doesn't work.

Let's try 2 x 315 + 1: 631 ÷ 11 = 57.36, and this doesn't work.

Let's try 3 x 315 + 1: 946 ÷ 11 = 86, and this works, and is the answer.

Workings

Hint
Remember that you have the same number of each coin.

Answer
134 of each coin.

Reasoning
We have equal numbers of 2p, 5p, 10p, and 20p.

And 2p + 5p + 10p + 20p = 37p.

There are 134 lots of 37p in £49.58.

Double-Checking
134 x 37 = 4958.