Question

Solve this.. ◻➕◻➕◻➕◻➕◻=30 Fill the boxes using (1, 3, 5, 7, 9, 11, 13, 15) U can also repeat the numbers. This question came in UPSC Final Exams held in Dec 2013. You will be glad to note that only Gaurav Agarwal (IAS Topper) could solve it.

Answer 1

(15-9)+(13-7)+(11-5)+(9-3)+(7-1)=30

Answer 2

Gaurav Agrawal answered very intelligently and using his imagination.         -- really for this question is asked so many times.. all credit goes to him.

you can answer this question in many ways using the factorial function.

3! + 3! + 3! + 3! + 3!      = 30 
   3! + 1 + 3 + 9 + 11          = 30
       1 + 5 + 7 + 3! + 11               = 30
             3! + 3! + 3! + 11 + 1             = 30
                 3! + 3! + 11 + 5 + 1               = 30
            11+ 1 + 1 + 3! + 11              = 30
       15 + 3 + 3 + 3 + 3!              = 30
     13 + 1 + 1 + 9 + 3!            = 30
         13 + 1 + 3 + 7 + 3!            = 30
               13 + 5 + 3 + 3 + 3!            = 30

If  one can use /, * , exponent and other operators, then you can get more answers too.  Question does not say anything about the operators.

  5 * 3 + 13 + 1 + 1 = 30
     13 + 15 + 3! - 3 - 1 =    30
          15! / 13! / 7 * 1 * 1  =  30
               5!  / 3!  + 1 * 3 + 7 = 30
                      7 * 5  - 3 - 1 - 1  =  30
                   9 * 7 / 3 + 9 * 1 =  30
          3³ + 1 + 11 - 13 * 1  = 30
     5³ / 15 * 3 + 5 * 1 = 30  
 3 * 15 - 11 - 3 - 1 = 30

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You need one operator for which the result is an even number with an input being an odd number.  Factorial is one.  Probably there are other operators too.