Open-ended - With worked solutions · SET 3

Three men are playing dice, each using different numbers. Each die has three numbers, each repeated (so each number appears on two faces). The men can choose their numbers. A should beat B, B should beat C, and C should beat A. What numbers should each die have?

A census taker called at a man's house and asked, "What are the ages of your 3 daughters?" The man said, "If you multiply their ages together it equals 72, and if you add them it equals your door number." The census taker said, "Well, if you cannot give me further information, I still don't know." The man said, "Well, my eldest daughter has a dog with a wooden leg." The census taker said, "I know now." What were their ages? Explain.

In the ring diagram, find the rule for the outer ring and for the inner ring. What are X and Y?

In the number pyramid, find the rule that gives the numbers on the bottom line. What are a, b, c and d?

Find the pattern in the table and give the values of A, B and C.

A billiard table is a rectangle whose sides are whole numbers, with just four pockets, one in each corner. A ball shoots out of one of the pockets at an angle of 45° to the sides. Will it keep bouncing around the table for ever, or finish up in one of the pockets? Explain.

In the two calculations shown, X and Y stand for the same digits each time. What are X and Y?

While driving his two young sons to the seaside, Dad had an idea to keep the boys busy. He invited each of them to choose a digit from 0 to 9 and to watch for it on the number plates of oncoming cars, promising a prize to the first one to spot his digit twenty times. Jimmy chose 0 and Freddie chose 1. Why was Freddie more likely to win than Jimmy?

If 6 3 5 4 2 becomes 5 2 6 3 4, what does B C D E F become (using the same rearrangement)?

Three married couples visit a casino. The men are John, Ernie and Oswald; the women are Alice, Betty and Marjorie. Each of the six gambles independently, and they agree to stop when each couple's gain or loss reaches £200. All three husbands lose, but each couple wins exactly £200 overall. Each person played as many single games as the average number of pounds he or she won or lost per game. Ernie lost £504 more than John. Betty won £2,376 more than Marjorie. Who is married to whom?

What are X and Y?

What are X and Y?

What is the value of X in each of the three diagrams A, B and C?

Give the values of X and Y.

Which car goes into which road? (Each car's number plate is shown on the car; each road has a number on its sign.)

Sheffield is 100 miles from Worcester. At 1 pm train A leaves Sheffield for Worcester at a constant 30 mph. One hour later train B leaves Worcester for Sheffield at a constant 40 mph. Each train makes only one stop, at a station 10 miles from its starting point, and stays there for 15 minutes. Which train is nearer to Sheffield when they meet?

What two terms complete this series?

What are X and Y?

Two square floors were covered with 12-inch (1 foot) square tiles. 850 tiles were used in total. Each side of one floor was 10 feet longer than each side of the other floor. What were the dimensions of the two floors?

The box weights are combined as shown. How much does each box weigh?