Maths Puzzles

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A farmer wants to cross a river and take with him a wolf, a goat, and a cabbage.

There is a boat that can fit himself plus either the wolf, the goat, or the cabbage.

If the wolf and the goat are alone on one shore, the wolf will eat the goat.

If the goat and the cabbage are alone on the shore, the goat will eat the cabbage.

To get everyone across, who will be with the farmer in the last trip?

You have three bags, each containing two marbles.

Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.

You pick a random bag and take out one marble.

It is a white marble.

What is the probability that the remaining marble from the same bag is also white?

The cold faucet in my bath lets the water in at the rate of 15 liters per minute.
The hot faucet fills the bath at the rate of 10 liters per minute.
The plug hole lets the water out of the bath at the rate of 12 liters per minute.

The bath holds a maximum of 520 liters.

I turn both faucets on, but forget to put the plug in. After how many minutes will the bath begin to overflow?

• 25 mins

• 40 mins

• 50 mins

• 65 mins

Rachel, Chan, and Sue work at a grocery store that sells pens, erasers, and pencils. 

Rachel says, "Seven pens and five erasers cost the same as six pencils.

Chan says, "Four pens and nine pencils cost the same as five erasers.

Sue says, "Six pencils and three erasers cost the same as four pens.

Only one is lying. Can you tell us who?

• Rachel
• Chan

• Sue
• Nobody

You arrive at a fork in the road and need to choose the correct path that leads to your destination.

There are two people standing at the fork, and you know that one must be a knight and the other must be a knave.

A knight will always tell the truth whereas a knave will always lie.

What single question could you ask one of the people to determine the correct path, A or B?

• Should I choose path A?

• What path would the other tell me to choose?

• Should I choose path B?

• Which is the correct path?