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'.)
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.)
AB × CD = ADCB (The same 4 digits appear on both sides of the = sign.)
What are the four digits?
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.)