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?

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.

Puzzle 398

Place letters into the grid such that every row, column, and 2x2 block has letters (in any order) that form a common word.

Each letter is only used once, and no letter is repeated in the rows/cols/blocks.

Across: CADS, YOLK, DATE, PIGS
Down : GLAD, STAY, COPE, SKID
Boxes : LADY, SOCK, STAG, PIED
Note : Other anagrams of these words are OK as long as they don't change the answer grid.

Puzzle 399

During the recent BrainBashers football competition, 5 schools were competing.

Each school played each other once, with 2 points for a win, 1 point for a draw, 0 points if they lost.

Here are the final points after all of the matches:

There were 5 teams in the league, therefore there were a total of possible 10 games. Each game distributed 2 points to the two teams.

Therefore, there were a total of 20 points available to the league, the results shown add to 17, leaving the remaining 3 to Fulton.

Puzzle 400

Using the BrainTracker grid below, how many words can you find? Each word must contain the central O and no letter can be used twice. The letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?