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 '13...... You will be glad to note that only Gaurav Agarwal could solve it.

Answer 1

The sum of three odd numbers gives an odd number
So, the sum of 3 given odd numbers doesnt results 30
So, it is an impossible factor
here we can't use 3! too
because 3! [3×2×1] results a even number 6
so we cant use it.
If there will be an allowance of factorials, then the answers will be
3!+1+5+7+11=30
3!+1+3+7+13=30

Answer 2

Gaurav Agrawal (IAS) answered very intelligently in 2014 using his imagination as 3! + 3! + 3! + 3! + 3! = 30  This question is asked so many times.. all credit goes to him.  The following ways are my suggestions.
I can answer this question in many ways using the factorial function.  3 ! => 3 factorial. it is a mathematics operator like + or /.. 3 ! = 3 * 2 * 1 = 6.
   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

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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.