Puzzle 11

Which is larger, the number of seconds in a day or the number hours in 10 years?

 [Ref: ZLCF] © Kevin Stone [Protected Puzzle]

Hint: Do leap years make a difference?

Answer: Hours in 10 years.

In a day there are 60 x 60 x 24 seconds = 86,400 seconds.

In 10 years there are 10 x 365 x 24 hours = 87,600 hours, which even without the leap years is already the larger number.

Puzzle 12

Due to rumours that there was a world shortage of chewing gum, everyone was stocking up on packs. By the time I'd got to the store, they had sold out!

However, there were two people at the till who had bought 4 and 5 packs respectively and they kindly offered to share their packs with me. After the sharing, we all had the same number of packs each and I paid them $9 for my packs. How did they share the $9 between them?

 [Ref: ZNBH] © Kevin Stone [Protected Puzzle]

Hint: The answer is not $4 and $5.

Answer: $3 and $6. As there were 9 packs in total, we each received 3 packs. The first person therefore gave me 1 pack, and the second person gave me 2 packs. So the money had to be shared in the same ratio, 1:2.

Puzzle 13

I travelled from London to Glasgow last week at 60 miles per hour, I had filled my petrol tank just before I left, so it was full with 25 gallons. Unfortunately, my petrol tank sprang a leak immediately and I only managed to drive 300 miles before I ran out of petrol. My car does 30 miles per gallon, how fast was I losing petrol through the hole?

 [Ref: ZFAU] © Kevin Stone [Protected Puzzle]

Hint: How much petrol did I use driving?

Answer: 3 gallons per hour. I drove 300 miles at 30 miles per gallon, so I used 10 gallons. Which means I lost the other 15 gallons. I drove the 300 miles at 60mph, which took me 5 hours. So I lost 15 gallons of petrol in 5 hours = 3 gallons per hour.

Puzzle 14

The island of Elbonia have a rather eccentric postal system. Postage for an item can be anything from 1 dinar to 15 dinari, and you must use exact postage. Frustratingly, there is only space on the envelopes in Elbonia to attach a maximum of three stamps. What is more, they only have three different denominations of stamps, can you work out what they are?

 [Ref: ZSMS] © Paul Bostock and Elliott Line
This puzzle appeared in Mensa's EnigmaSig and is used with permission.

Hint: How can we post something that costs 1 dinari? What about 15 dinari?

Answer: 1 dinari, 4 dinari, 5 dinari.

We must be able to create 1, so we must have a 1 dinari stamp. As we need to create all numbers from 1 up to 15 it's easiest to think about the start and end. We must have 1 to create 1, and we also need 5 to create 15 (5 + 5 + 5). The missing value can't be above 5 otherwise we can't make 4.

If the other value was 1 or 2, there would be no way to make 13. If the other value was 3 or 5, there would be no way to make 12. So 4 is the only value it could be:

1 = 1
2 = 1 + 1
3 = 1 + 1 + 1
4 = 4
5 = 5
6 = 5 + 1
7 = 5 + 1 + 1
8 = 4 + 4
9 = 5 + 4
10 = 5 + 5
11 = 5 + 5 + 1
12 = 4 + 4 + 4
13 = 5 + 4 + 4
14 = 5 + 5 + 4
15 = 5 + 5 + 5

Puzzle 15

My local bus company has recently expanded and no longer has enough room for all of its buses. Twelve of their buses have to be stored outside. If they decide to increase their garage space by 40%, this will give them enough room for all of their current buses, plus enough room to store another twelve in the future. How many buses does the company currently own?

 [Ref: ZWOL] © Kevin Stone [Protected Puzzle]

Hint: A tricky puzzle that will need a little algebra (or clever thinking).

Answer: 72 buses: they have enough room for 60 of these, expanding the 60 capacity by 40% will give them enough room for 84, which we know is 12 more spaces than they currently need.

If they have B buses and S spaces before the expansion, they have enough room for:

           S = B - 12        [1]

After the expansion they have more spaces, and enough room for:

 S + 0.4 x S = B + 12        [2]

Rewriting [2] as:

        1.4S = B + 12

and again as

           B = 1.4S - 12     [3]

We can rewrite [1] as:

           B = S + 12        [4]

Making [3] = [4] we have:

   1.4S - 12 = S + 12

Subtracting S from both sides gives:

   0.4S - 12 = 12

Adding 12 to both sides gives:

        0.4S = 24

Multiplying by 10 and dividing by 4 on both sides gives:

           S = 60

Using S = 60 in [4] gives B = 72. QED.