Working systematically

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Can you substitute numbers for the letters in these sums?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Suppose you are a bellringer. Can you find the changes so that, starting and ending with a round, all the 24 possible permutations are rung once each and only once?