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 39
Оглавление148. A 1000-digit number
What is the largest number of digits that can be erased from the 1000-digit number 201820182018 … 2018 so that the sum of the remaining digits is 2018?
149. Gardeners at work
It takes four gardeners four hours to dig four circular flower beds, each of diameter four metres.
How long will it take six gardeners to dig six circular flower beds each of diameter six metres?
150. Overlapping squares
The diagram shows four overlapping squares that have sides of lengths 5 cm, 7 cm, 9 cm and 11 cm.
What is the difference between the total area shaded grey and the total hatched area?
151. What can T be?
Each of the numbers from 1 to 10 is to be placed in the circles so that the sum of each line of three numbers is equal to T. Four numbers have already been entered.
Find all the possible values of T.
152. Increases of 75%
Find all the two-digit numbers and three-digit numbers that are increased by 75% when their digits are reversed.
153. Three groups
For which values of the positive integer n is it possible to divide the first 3n positive integers into three groups each of which has the same sum?
154. A board game
Two players, X and Y, play a game on a board that consists of a narrow strip that is one square wide and n squares long. They take turns in placing counters that are one square wide and two squares long on unoccupied squares on the board.
The first player who cannot place a counter on the board loses. X always plays first, and both players always make the best available move.
Who wins the game in the cases where n = 2, 3, 4, 5, 6, 7 and 8?
