64. | A 'Harshad number' has been defined as a number which can be divided exactly by the sum of its digits. For example: 1729 is a Harshad number since 1 + 7 + 2 + 9 = 19 and 1729 can be divided exactly by 19.
Find the smallest Harshad number which is divisible by 13
(Harshad numbers were defined by D R Kaprekar (a mathematician from India) who also gave us |
65. |
Each of the letters A, B, C, D, E is used to represent a single digit in these two statements.(Same letter = same digit.)
A + B = C |
What is the value of B + D ? |
66. | Two planes fly once around the world together. They both fly at a constant distance above the surface of the Earth, one above the other. On completion, one of the planes has travelled two kilometres further than the other. (Assume the Earth is a perfect sphere.)
How far apart (in metres) were the two planes? |
The winner of Competition #21 was Caroline Lines of Cardiff
The answers were:
61. | 1/1/01 |
62. | 22 + 2 or 3^3 - 3 or 9 x sqrt(9) - sqrt(9) or 4 + 4! - 4 |
63. | 1683 different ways. |