Cleave Books
Puzzle Trio 22

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 whose digit-sum is 13

(Harshad numbers were defined by D R Kaprekar (a mathematician from India) who also gave us 'Kaprekar's Constant'.
The word 'Harshad' comes from the Sanskrit language and means 'great joy'.)

65. Each of the letters A, B, C, D is used to represent a single digit in this statement.
(Same letter = same digit; and all digits are different.)

(The same 4 digits appear on both sides of the = sign.)

What are the four digits?

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?

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