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 (IAS Topper) could solve it.

Answer 1

i)   3!+1+3+13+7=30              [ If we solve by factorial method]
ii)   3!+3!+3!+3!+3!=30
     [3!=3×2×1=6]

[without factorial method]
Odd nos added for odd nos. of time will always give an ODD NUMBER.
Odd nos added for even no of time will give an EVEN NUMBER.

Answer 2

3!+3!+3!+3!+3!=30 but if we take 1!+1!+1!+1!+1!=5 which is less than 30