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 38
Оглавление141. Joey’s and Zoë’s sums
Joey calculated the sum of the largest and smallest two-digit numbers that are multiples of three. Zoë calculated the sum of the largest and smallest two-digit numbers that are not multiples of three.
What is the difference between their answers?
142. When is the party?
Six friends are having dinner together in their local restaurant. The first eats there every day, the second eats there every other day, the third eats there every third day, the fourth eats there every fourth day, the fifth every fifth day and the sixth eats there every sixth day. They agree to have a party the next time they all eat together there. In how many days’ time is the party?
143. A multiple of 11
The eight-digit number ‘1234d678’ is a multiple of 11.
Which digit is d?
144. Two squares
ABCD is a square. P and Q are squares drawn in the triangles ADC and ABC, as shown.
What is the ratio of the area of the square P to the area of the square Q?
145. Proper divisors
Excluding 1 and 24 itself, the positive whole numbers that divide into 24 are 2, 3, 4, 6, 8 and 12. These six numbers are called the proper divisors of 24.
Suppose that you wanted to list in increasing order all those positive integers greater than 1 that are equal to the product of their proper divisors. Which would be the first six numbers in your list?
146. Kangaroo game
In the expression
the same letter stands for the same non-zero digit and different letters stand for different digits.
What is the smallest possible positive integer value of the expression?
147. A game with sweets
There are 20 sweets on the table. Two players take turns to eat as many sweets as they choose, but they must eat at least one, and never more than half of what remains. The loser is the player who has no valid move.
Is it possible for one of the two players to force the other to lose? If so, how?
