Random Puzzles 

Workings

Hint
Think about the first digits of the numbers.

Answer
There are more 2's because of the numbers beginning with 20,000.

Workings

Hint
Try working backwards.

Answer
175 miles.

The total distance was 180 miles, but as I still had 5 miles to go, the required answer is 175 miles.

Reasoning
Let's try working backwards.

Day 4: I travelled ³/₄, which means that the other ¹/₄ was 5 miles – so 20 miles were left at the start of day four.

Day 3: I travelled ²/₃, which means that the other ¹/₃ was 20 miles – so 60 miles were left at the start of day three.

Day 2: I travelled ¹/₂, which means that the other ¹/₂ was 60 miles – so 120 miles were left at the start of day two.

Day 1: I travelled ¹/₃, which means that the other ²/₃ was 120 miles – so 180 miles were ahead at the start of day one.

The full distance was therefore 180 miles, but we were asked how many miles I had travelled so far, and as I still had 5 to go the answer is 175 miles.

Double-Checking
Start distance: 180 miles.

Day 1: I travelled ¹/₃ of the distance (60 miles), leaving 120 miles.

Day 2: I travelled ¹/₂ of the distance (60 miles), leaving 60 miles.

Day 3: I travelled ²/₃ of the distance (40 miles), leaving 20 miles.

Day 4: I travelled ³/₄ of the distance (15 miles), leaving 5 miles.

Workings

Hint
Which letters are missing?

Answer
The letter was written on a typewriter that has a problem with the top row of letters – they did not print correctly. The letter should have read:

Dear Kevin,

I would like to complain about the top row of my typewriter.

These letters do not appear to be working correctly.

As you can see, they are missing from this document.

I would be very grateful if you could correct this problem immediately.

Kind regards.

Sam South.

Workings

Hint
There are over 20 mistakes.

Answer
21.

Reasoning
Many years ago, before modern education in the new millennium, one problem in schools was basic spelling and grammar. To combat this and raise achievement, teachers were advised to start at the very beginning, at the youngest age. Once they had managed to breathe new life into lessons, progress came quickly, success was then guaranteed. How many spelling errors would modern scholars identify in this passage?