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 18
Оглавление50. A stack of cubes
Katie writes a different positive integer on the top face of each of the fourteen cubes in the pyramid shown.
The sum of the nine integers written on the cubes in the bottom layer is 50. The integer written on each of the cubes in the middle and top layers of the pyramid is equal to the sum of the integers on the four cubes underneath it.
What is the greatest possible integer that she can write on the top cube?
51. The largest remainder
Gregor divides 2015 successively by 1, 2, 3, and so on up to and including 1000. He writes down the remainder for each division.
What is the largest remainder he writes down?
52. Go on and on and on and on
In this addition, G, N and O represent different digits, none of which is zero.
What are the numbers in this sum?
53. A list of primes
Alice writes down a list of prime numbers less than 100, using each of the digits 1, 2, 3, 4 and 5 only once and using no other digits.
Which prime number must be in her list?
54. Continue the pattern
The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle.
How many small shaded squares are needed to build the tenth pattern in the sequence?
55. How many codes?
Peter has a lock with a three-digit code. He knows that all the digits of his code are different, and that if he divides the second digit by the third and then squares his answer he will get the first digit.
What is the difference between the largest and smallest possible codes?
56. A word product
What is the value of P + Q + R in the multiplication shown?
