Mathematical Puzzles 

Workings

Hint
What must the middle temperature be? Remember that the temperature are in degrees Celsius.

Answer
The temperatures were -6, -2, 2, 6, 10 °C.

Each day increased by a steady 4 degrees.

Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).

Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).

If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.

If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does matches all of the requirements.

If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.

Any larger increase makes the product even larger, so we can stop checking.

So the only possible answer is -6, -2, 2, 6, 10.

Workings

Hint
Try working backwards.

Answer
£98.82.

Reasoning
At the end I was left with £32.94, which was half of my remaining money, so before buying the trousers I must have had £65.88.

Again, this was half of my money, so before buying the jacket I must have had £131.76 at the start.

As I now had £32.94 remaining, I must have spent £98.82.

Double-Checking
I started with £131.76, and I spent £65.88 on a new jacket, and then £32.94 on the trousers, a total spend of £98.82.

Workings

Hint
Think of the whole alphabet, and not just the vowels (AEIOU).

Answer
8,300.

Each letter of the country is worth 100 miles based on its position in the alphabet.

Therefore, Germany = 7 + 5 + 18 + 13 + 1 + 14 + 25 = 83 x 100 miles.

Workings

Hint
I bought at least 8 of each stamp.

Answer
Eight lots of 11p, 17p and 21p, and nine lots of 3p and 9p.

Reasoning
For three denominations of stamp I was asked to buy 8 of each, and for the other two denominations I had to buy 9 of each.

So I had to buy at least 8 of all five denominations.

This would be for a total of 8 x (3 + 9 + 11 + 17 + 21) = 488p = £4.88.

The remaining 12p has to buy the remaining 2 stamps, which must have been 3p and 9p.

Double-Checking
9 x 3 = 27
9 x 9 = 81
8 x 11 = 88
8 x 17 = 136
8 x 21 = 168

For a total of 27 + 81 + 88 + 136 + 168 = 500p = £5.