Working systematically

In the café, your ice cream selection can't include a combination that someone else has chosen. What could these seven children have chosen?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.