Anand's Number
There is a 4-digit number whose digits are in descending order and follows some interesting properties:
i) The sum of the first, third, and fourth exceeds the second by 8
ii) The sum of the squares of the first and the second exceeds the sum of the squares of third and the fourth by 36
iii) The sum of the products of the first and second, and of the third and fourth is 42
iv) The cube of the first is equal to the sum of the cubes of the second, third and the fourth.
The answer is 6543.
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1 solution
You can start with the third condition where sum of product of first two numbers and last two is equal to 42. It provides a constraint that first two numbers (a,b) are less than (7,6). Now, take the other pairs (7,5), (7,4), (7,3), (6,5), (6,4) and fill the value of (c,d). --> 6543