# Puzzle | Fill Brackets ( )+( )+( )+( )+( ) = 30

( ) + ( ) + ( ) + ( ) + ( ) = 30

This is what you have for equation and following are the numbers that you can use to fill in the brackets:

1, 3, 5, 7, 9, 11, 13 and 15.

You can repeat the no. if required. The resulting sum should be 30.

**Solution:** The main issue here is that an addition of odd numbers for odd number of times will result in an odd number. So, in no way will you get an even number like 30 by adding these odd numbers but we can apply other mathematical operations inside brackets and get the answer.

**Method 1:** We can achieve the result of 30 by using the ‘-‘ operator inside the brackets with the digits.

(15 – 9) + (13 – 7) + (7 – 1) + (9 – 1) + (13 – 9) = 30

If you solve inside the brackets you will get the following equation

6 + 6 + 6 + 8 + 4 = 30

**Method 2:** the result of 30 can also be achieved by using the factorial of number. Since factorial of 3! = 6. If we add 3! five times it will result in 30.

(3!) + (3!) + (3!) + (3!) + (3!) = 6 + 6 + 6 + 6 + 6 = 30

Same question with variation may be asked like () + () + () + () + () = 5. Use of 0 is allowed here.

Same trick of factorial can be applied here, since value of 0! = 1.

Adding factorial 0 five times will result in 5.

0! + 0! + 0! + 0! + 0! = 5

1 + 1 + 1 + 1 + 1 = 5

**References: **https://www.bhavinionline.com/2014/09/fill-boxes-30/

This article is contributed by **RAJENDRA SINGH RAJPU**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Puzzle 1 | (How to Measure 45 minutes using two identical wires?)
- Puzzle 2 | (Find ages of daughters)
- Puzzle 3 | (Calculate total distance travelled by bee)
- Puzzle 4 | (Pay an employee using a 7 units gold rod?)
- Puzzle 13 | (100 Prisoners with Red/Black Hats)
- Puzzle 5 | (Finding the poisoned wine)
- Puzzle 6 | (Monty Hall problem)
- Puzzle 7 | (3 Bulbs and 3 Switches)
- Puzzle 8 | (Find the Jar with contaminated pills)
- Puzzle 9 | (Find the fastest 3 horses)
- Puzzle 10 | (A Man with Medical Condition and 2 Pills)
- Puzzle 11 | (1000 Coins and 10 Bags)
- Puzzle 12 | (Maximize probability of White Ball)
- Puzzle 14 | (Strategy for a 2 Player Coin Game)
- Puzzle 15 | (Camel and Banana Puzzle)