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 29

Week 15

99. Folded shapes

A sheet of A4 paper (297 mm × 210 mm) is folded once and then laid flat on the table.

Which of these shapes could not be made?

[SOLUTION]

100. Einstein’s clocks

Albert Einstein is experimenting with two unusual clocks that both have 24-hour displays. One clock goes at twice the normal speed. The other clock goes backwards, but at the normal speed. Both clocks show the correct time at 13:00.

What is the correct time when the displays on the clocks next agree?

[SOLUTION]

101. The total area

The diagram shows three semicircles, each of radius 1.

What is the size of the total shaded area?

[SOLUTION]

102. How many weeks?

How many weeks are there in 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 minutes?

[SOLUTION]

103. A platinum question

Platinum is a very rare metal, even rarer than gold. Its density is 21.45 g/cm³. Assuming that the world production has been about 110 tonnes for each of the past 50 years, and negligible before that, which of the following has a comparable volume to that of the total amount of platinum ever produced?

(a) a shoe box;

(b) a cupboard;

(c) a house;

(d) Buckingham Palace;

(e) the Grand Canyon

[SOLUTION]

104. Underlining numbers

Ten different numbers (not necessarily integers) are written down. Any number that is equal to the product of the other nine numbers is then underlined.

At most, how many numbers can be underlined?

[SOLUTION]

105. Placing draughts

Barbara wants to place draughts on a board in such a way that the number of draughts in each row is equal to the number shown at the end of the row, and the number of draughts in each column is equal to the number shown at the bottom of the column. No more than one draught is to be placed in any cell.

In how many ways can this be done?

[SOLUTION]