Working systematically

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?

A 1×2×3 block is placed on an 8×8 board and rolled several times.... How many squares has it occupied altogether?

Can you find squares within a number grid whose entries add up to an even total?

Can you find a number and its double using the digits $1$ to $9$ only once each?

What could be the scores from five throws of this dice?

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?

The digits 1-9 have been written in the squares so that each row and column sums to 13. What is the value of n?

Can you choose one number from each row and column in this grid to form the largest possibe product?