Problems

You meet a couple, Dan and Daisy. Dan asks Daisy “Are you the kind who could ask me whether I am a Crick?"
What can be deduced about Dan and Daisy?

You meet an alien called Bobby. He asks you “Am I the kind who could ask whether the wizard is the kind who could ask whether I am the wizard?"
Do you now know for sure who the wizard is?

You then meet a strange alien who asks you “Am I the kind who could ask you the question I am now asking?"
What can be said about her?

You meet three friends: Alex, Bernie and Carol. Alex asked Bernie “Are you the kind who could ask Carol whether she is the kind who could ask you whether you two are of different kinds?".
You might realise that it is only possible to deduce the kind of one of the three friends. Which one and are they a Crick or a Goop?

You meet an alien called Charlie. He asks you “Are the wizard and I the same kind?"
Who is the wizard?

a) Mr Smith has seven children. He wants to send three of them to run some errands on a Saturday. We will send the first child at 1pm, the second child at 2pm and the third one at 4 pm. In how many ways can he choose them?
b) The children decided to actually go run all the errands together at 1pm, instead of going separately. Knowing this, in how many ways can Mr Smith select three of them to run the errands?

Katie is making a bouquet. She has $12$ different flowers available, but wants her bouquet to be composed of exactly $5$ of them. The order of the flowers in the bouquet doesn’t matter. In how many ways can she do this?

We have $6$ digits available: $1,3,4,5,7$ and $9$. We wish to make a $3$-digit number with different digits but only using these $6$ digits. How many ways are there of doing this? What if we want the digits within the number to be arranged in an ascending order - how many numbers are left?

David has $15$ video games in boxes on his shelf. His family is visiting his aunt next week. He was asked to pick only $4$ games to be able to play on his cousin’s computer. In how many ways can he do this?

Katie is making a bouquet again. She has $12$ flowers, but this time she wants to use not $5$, but $7$ flowers for a bouquet. In how many ways can she do this? How is this answer related to the answer to the previous question about Katie? Why?