Welcome to Day 8

This topic may be tricky so give close attention to this one.

We again follow the base system - Not exactly, but depending on the base calculation will differ.

Consider base 10

Cube for 13
13 = (13 + 3 x 2)/(9 x 3)/3 x 3 x 3
     = 19/27/27 (But since the base is 10 only one number will remain in each left hand side.
Therefore answer is = 19/29/7
                            = 21/9/7.

Steps involved

  1. First we double the excess number from the base 10 and add to the original number i.e. 13- 10 = 3. Then 3 x 2(double the excess) + 13 (original number) = 19
  2. Then we subtract 13 from base, get 3, which we multiply with 9 ( the excess number of the left hand side number minus the base i.e. 19 -10 ). So basically - excess from original number from 10 x excess from the left number which we got in step 1. We get 3 x 9 = 27.
  3. Then we take the cube of the unit digit of the original number.
  4. And doing the required calculation for the base 10, we get the answer 2197.

Cube for 15
15 = (15 + 5 x 2)/(15x5)/5 x 5 x 5
     = 25/75/125
     =25/87/5
     =33/7/5

Steps involved

  1. First we double the excess number from the base 10 and add to the original number i.e. 15- 10 = 5. Then 5 x 2 + 15 (original number) = 25
  2. Then we subtract 15 from base, get 5, which we multiply with 15 ( the excess number of the left hand side number minus the base i.e. 25 -10.) So basically, 15 x 5 = 75.
  3. Then we take the cube of the unit digit of the original number.
  4. And doing the required calculation for the base 10, we get the answer 3375.

97 = (97 – 2 x 3)/(-3 x -9)/-3 x -3 x -3
     = 91/27/-27
     =91/26/73

Steps involved

  1. First we double the excess number from the base 100 and subtract to the original number i.e. 100 - 97 = -3. Then -3 x 2 -3 (original number) = -9
  2. Then we subtract 97 from base, get -3, which we multiply with -9 ( the excess number of the left hand side number minus the base i.e. 100 - 91.). So basically, -3 x -9 = 27.
  3. Then we take the cube of 100 – 97.
  4. And doing the required calculation for the base 100, we get the answer 912673.

In similar manner,

52 = (52 + 2 x 2)/(2 x 6)/08
     = 56/12/08
     = 14/06/08

104 = (100 + 3 x 4)/3 x 4 x 4/4 x 4 x 4 = 112/48/64

This may be a tough lesson and with the limitation it is not easy to explain this method only through text. But I am sure once you go through the above steps a few more time, then you will easily get the hang of this method. So good luck and make sure you practice.

I hope this lesson was fun and you enjoyed it as much as I enjoyed writing it down for you!

See you tomorrow.

Rahul Makhija

If you have missed any of the previous days, then you can visit them now:

Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7

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