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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

Rule of Three

Age 11 to 14 Challenge Level:

"I quite agree with you," said the Duchess, " and the moral of that is - 'Be what you would seem to be' - or, if you'd like it put more simply - 'Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise."

If it takes $4$ men one day to build a wall, how long does it take $60$ $000$ men to build a similar wall?