Mental calculations

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Can you use the clues to complete these 4 by 4 Mathematical Sudokus?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

A Sudoku with clues given as sums of entries.

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?