Random Puzzles 

Workings

Hint
Try to rotate them around in your head, but watch out for mirror images.

Answer
A, D, and E.

Workings

Hint
Start on any square, and see how far you can get.

Answer
Start from the 1L on the fifth row down and second column across.

Workings

Hint
Think about the 40%, and how many buses that represents.

Answer
72 buses.

Reasoning
The garage is currently full, with 12 more buses outside.

If we increase the garage space by 40%, there will be enough space to house those 12 buses, plus 12 more in the future, a total of 24 buses.

This means that 40% of the current garage capacity is 24 buses.

Therefore, 10% of the current garage capacity is 6 buses.

Therefore, 100% of the current garage capacity is 60 buses.

So, the current garage holds 60 buses, and there are 12 more outside.

Therefore, we have a total of 72 buses.

Double-Checking
They currently have 72 buses, 12 of which are outside, so 60 are inside.

Increasing the garage space of 60 buses by 40% will give room for 60 x 1.4 = 84 buses.

Which is the 72 they currently own, with space for 12 more buses in the future.

This confirms the answer.

Workings

Hint

Answer
23.

Reasoning
By likely, we mean greater than 50% chance.

With one person there is a 0 percent chance that you'll have two people with the same birthday.

With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).

With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).

Notice that with each additional person added, the probability that they shares a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.

We keep adding people until the %age is greater than 50%.

When we have 23 people the %age is 50.729%.