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 33
Оглавление120. Gluing cubes
A cube is made by gluing together a number of unit cubes face-to-face. The number of unit cubes that are glued to exactly four other unit cubes is 96.
How many unit cubes are glued to exactly five other unit cubes?
121. Mr Gallop’s ponies
Mr Gallop has two stables that each initially housed three ponies. His prize pony, Rein Beau, is worth £250 000. Rein Beau usually spends his day in the small stable, but when he wandered across into the large stable, Mr Gallop was surprised to find that the average value of the ponies in each stable rose by £10 000.
What is the total value of all six ponies?
122. Making a square
I have two types of square tile. One type has a side length of 1 cm and the other has a side length of 2 cm.
What is the smallest square that can be made with equal numbers of each type of tile?
123. How many pairs?
How many pairs of digits (p, q) are there so that the five-digit integer ‘p869q’ is a multiple of 15?
124. What is the product?
Lucy wants to put the numbers 2, 3, 4, 5, 6 and 10 into the circles so that the products of the three numbers along each edge are the same, and as large as possible.
In how many ways can this be done?
125. A five-team league
Five teams played in a competition and every team played once against each of the other four teams. Each team received three points for a match it won, one point for a match it drew and no points for a match it lost.
At the end of the competition the points were as follows:
| Yellows | 10 |
| Reds | 9 |
| Greens | 4 |
| Blues | 3 |
| Pinks | 1 |
How many of the matches resulted in a draw?
What were the results of the Greens’ matches against the other teams?
126. A mini crossnumber
The solution to each clue of this crossnumber is a two-digit number, not beginning with zero.
Across
1. A triangular number
3. A triangular number
Down
1. A square
2. A multiple of 5
In how many different ways can the crossnumber be completed correctly?
