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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.

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 107

As my birthday approaches I start to collect leaves - a little bizarre perhaps, but I enjoy it!

On the first day of the month I collect 1 leaf, on the second day I collect 2 leaves, the third day I collect 3 leaves, and so on.

By my birthday I will have collected 276 leaves altogether. On which day of the month is my birthday?

The easiest way to solve this puzzle is to use Q1 to check the logic.

If Q1's answer was A, this tells us that Q2's answer is B, which tells us Q3's is D, which tells us Q4's answer is B, which tells us Q1's answer is C. A contradiction.

If Q1's answer was B, this tells us that Q2's answer is A, which tells us Q3's is C, which tells us Q4's answer is C, which tells us Q1's answer is A. A contradiction.

If Q1's answer was C, this tells us that Q2's answer is D, which tells us Q3's is A, which tells us Q4's answer is D, which tells us Q1's answer is B. A contradiction.

If Q1's answer was D, this tells us that Q2's answer is C, which tells us Q3's is B, which tells us Q4's answer is A, which tells us Q1's answer is D. Which is correct, and therefore the correct answer.

Puzzle 110

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

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