• # These cubes are Ramanujan's favourite.

Yesterday (April 26,1920) being the death anniversary of the genius Srinivasa Ramanujan, I thought of sharing this interesting number theory. His Professor once said that every positive integer is a friend of him and one day he visited him in the hospital and remarked that he has taken the taxi with the number 1729 and said it is a dull number. But immediately Ramanujan replied that this number is the smallest integer that can be represented as sum of two cubes of two ways that is 1 cube + 12 cubes and 9 cubes + 10 cubes.

I find this cube root to be interesting. So members may try all these operations and using three 2s,3s,4s,5s,6s,7s,8s and 9s to come with solution as 6.
• Here are a few possible solutions:

Solution 1:
6 = ?(5 + 5 + 5)
Using three 5s, we can add them together and take the cube root to get 6.

Solution 2:
6 = ?(9 + 9 - 6)
Using two 9s and one 6, we can add the 9s and subtract 6, then take the cube root to get 6.

Solution 3:
6 = ?(4 * 4 * 4) / 2
Using three 4s and one 2, we can multiply the 4s together and divide by 2, then take the cube root to get 6.

Solution 4:
6 = ?(8 * 8 / 2)
Using two 8s and one 2, we can multiply the 8s and divide by 2, then take the cube root to get 6.

Solution 5:
6 = ?(7 * 7 - 5)
Using one 7 and two 5s, we can multiply the 7 and subtract 5 twice, then take the cube root to get 6.

These are just a few examples. There may be many other solutions that use different combinations of digits and operations to represent 6 using three identical digits and cube root.

Learn one more language and you will feed your brain the top nutrition!
- Geeta

• 1. 2 cube + 2 square and then divide it by 2. The answer Will be 6
2. 3 to the power 4 divided by 3 cubes and then add 3. The answer will be six
3. 4 + 4 - square root of 4. The answer will be 6
4. 5 square + 5 and then divide with 5. The answer will be 6.
5. 6 + 6 -6 = 6
6. 7 - (7/7) = 6
7. cube root 8 + cube root 8 + cube root 8 = 6
8. (9 + 9) / square root 9 =6
I request the author to tell me whether I understood the concept or not.

drrao
always confident

• @Dr.Rao good attempt.For 2 it is simply 2+2+2 is 6. Also for 3 it is 3*3 minus 3 and others are really nice.

@Geeta it is like this you have to use identical numbers

Hope others may try.

Another interesting problem by Ramanujan like taxi number he did for house numbers too. Also simple addition he has done in his childhoof is adding 1 to 10 by placing 10 to 1 underneath 1 to 10 and adding comes to 11 10 times and 10 11s are 110 divided by 2 is 55.

Hope this kind of shortcuts help students as well as those who are taking competitive exams.

shasthranaam Ganitham moordhanisthitham

• Thank you Sarojah. I missed the first two simple steps and I tried using cubes and squares. Like this these days we are coming across many shortcuts. This is mainly due to social media and many people are posting their ideas there and it is getting circulated. That way social media is very useful.
drrao
always confident

• Yes Dr.Rao. Even for this you have come out with good options for 4,5,6 and 9. Even you may try different versions for these.

Others also please try for these numbers.

shasthranaam Ganitham moordhanisthitham