Multiple choice general knowledge math & puzzles

if a,b,c,d are 4 ditinct non zero positive integers such thatsum of cubes of first two nos. is equal to sum of cubes of last two nos. i.e.a^3+b^3=c^3+d^3then min. value of a+b+c+d is

  1. 30

  2. 32

  3. 31

  4. no such nos. possible
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The smallest solution to a^3 + b^3 = c^3 + d^3 with distinct positive integers is 1^3 + 12^3 = 9^3 + 10^3 = 1729. This is known as the Hardy-Ramanujan number or the smallest taxicab number. The sum is 1 + 12 + 9 + 10 = 32. Such numbers are possible and well-studied in number theory.

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