Sum of 3 odd numbers is 30 gaurav agarwal

Asked by admin @ 20/08/2021 in Math viewed by 365 People

SOLVE THIS ?

++ = 30Fill the boxes using(1,3,5,7,9,11,13,15)You can also repeat the numbersThis question came in UPSC final examhed in December 2013 at IndiaYou will be glad to note that onlyGaurav Agarwal (IAS Topper) could solve8:13 pm

Answered by admin @ 20/08/2021

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 $7$ .

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

$=7+3$

$=10$

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