Читать книгу The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind - Литагент HarperCollins USD, F. M. L. Thompson - Страница 22

Shuttle Challenge 1

In the Shuttle rounds of the Team and Senior Team Maths Challenges, each team of four students is divided into two pairs who sit at opposite ends of a table. One pair tackles questions 1 and 3; the other pair attempts questions 2 and 4. The numerical answer to question 1 is passed across the table to the other pair who need it to answer question 2, and so on. The answer that is passed on is called A in the subsequent question.

The teams have eight minutes to answer all four questions. They get bonus marks if they answer all the questions correctly within six minutes.

How long will it take you?

Question 1

What is the value of (4² + 5²) × 7²?

Question 2

[A is the answer to Question 1.]

At which number will the minute hand of a clock be pointing to (A + 1) minutes after midnight?

Question 3

[A is the answer to Question 2.]

John has three sticks that he has formed into a triangle. The length of each stick is a whole number of centimetres.

The length of one of the sticks is (A + 1) cm, and the length of another of the sticks is (A − 1) cm.

How many different possibilities are there for the length of John’s third stick?

Question 4

[A is the answer to Question 3.]

A pyramid with a polygonal base has A faces.

How many edges does the pyramid have?

[SOLUTION]