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 35

Week 19

127. Coins in a frame

The diagram shows 10 identical coins that fit exactly inside a wooden frame. As a result, each coin is prevented from sliding.

What is the largest number of coins that may be removed so that each remaining coin is still unable to slide?

[SOLUTION]

128. Cheetah v. snail

In a sponsored ‘Animal Streak’, the cheetah ran at 90 kilometres per hour, while the snail slimed along at 20 hours per kilometre. The cheetah kept going for 18 seconds.

Roughly how long would the snail take to cover the same distance as the cheetah?

[SOLUTION]

129. Memorable phone numbers

A new taxi firm needs a memorable phone number. They want a number that has a maximum of two different digits. Their phone number must start with the digit 3 and be six digits long.

How many such numbers are possible?

[SOLUTION]

130. How many games?

Cleo played 40 games of chess and scored 25 points.

A win counts as one point, a draw counts as half a point, and a loss counts as zero points.

How many more games did she win than lose?

[SOLUTION]

131. How many draughts?

Barbara wants to place draughts on a 4 × 4 board in such a way that the number of draughts in each row and in each column are all different. (She may place more than one draught in a square, and a square may be empty.)

What is the smallest number of draughts that she would need?

[SOLUTION]

132. To and from Jena

In a certain region these are five towns: Freiburg, Göttingen, Hamburg, Ingolstadt and Jena.

One day, 40 trains each made a journey, leaving one of these towns and arriving at another.

10 trains travelled either to or from Freiburg.

10 trains travelled either to or from Göttingen.

10 trains travelled either to or from Hamburg.

10 trains travelled either to or from Ingolstadt.

How many trains travelled either to or from Jena?

[SOLUTION]

133. Largest possible remainder

What is the largest possible remainder that is obtained when a two-digit number is divided by the sum of its digits?

[SOLUTION]