Question

SOLVE THIS ?
++ = 30
Fill the boxes using
(1,3,5,7,9,11,13,15)
You can also repeat the numbers
This question came in UPSC final exam
hed in December 2013 at India
You will be glad to note that only
Gaurav Agarwal (IAS Topper) could solve
8:13 pm​

Answer 1

Question

$\_\_+\_\_+\_\_=30$

Fill the box using 1, 3, 5, 7, 9, 11, 13, 15. You can repeat the numbers.

Keys

We can't obtain an even number 30 by just choosing three numbers, because the result is always odd. Let's think outside the box.

• Sol. 1

'Reversing' method.

• Sol. 2

Decimal numbers.

• Sol. 3

Borrowing numbers from other number systems.

Solution

Sol. 1

It is a commonly seen method in various riddle videos. So, here it is.

Reverse $9$ upside down to get $6$.

☆$6+9+15=30$

Sol. 2

Let us repeat the number below the decimal point.

☆$1.1+13.9+15=30$

Sol. 3

The number $(11)_{9}$ represents '11 in base 9.' It is just 10.

We have base 9.

☆$(11)_{9}+(11)_{9}+(11)_{9}=30$

Or, we could use base 7. $13_{7}$ is the number 10.

☆$(13)_{7}+(13)_{7}+(13)_{7}=30$

More information

In base 9, each digit value is a power of $9$.

$(11)_{9}=(10)_{9}+(1)_{9}$

$=9+1$

$=10$

Similarly, in base 7, each digit value is a power of $7$.

$(13)_{7}=(10)_{7}+(3)_{7}$

$=7+3$

$=10$

Answer 2

ANSWER

The sum of

three odd numbers gives an odd number

So, the

sum of 3 given odd numbers doesn't results 30

So, it

is an impossible factor

here we

can't use 3! too

because

3! [3x2x1] results a even number 6

SO we

can't use it.

If there will be an

allowance of factorials, then the

answers will be

3! + 15 + 9 =30

3! + 11

+ 13 = 30