Exploring and noticing

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Choose any three by three square of dates on a calendar page...

How many arm-wrestles will there be in the royal arm wrestling championship?

A pattern repeats every six symbols. What are the 100th and 101st symbols?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?

An examination paper is made from five pieces of paper. What is the sum of the other page numbers that appear on the same sheet as page 5?

One year there were exactly four Tuesdays and four Fridays in October. On what day of the week was Halloween.