Numbers, shapes and the idea of 16,777,216.

I like the number 24.  It seems like a very reliable number, doesn’t it?  You can build a rectangle, a square or even a triangle with it.

Rectangular wall – 2 towers with 12 coins each.

Square wall- 4 towers with 6 coins each.

Triangular wall – 3 towers with 8 coins each.

24 seems like the smallest number that could make a good defensive wall against any enemy. 12 seems like a poor defense and 36 seems too big a number to gather at a short notice during an invasion.

Nevertheless, 36 is a fascinating number; a tall hexagon making its appearance for the first time (the shorter version of which you see in 24 and 12). It may not make sense to you as to why I do not consider 30 as a tall hexagon; you can decide for yourself by building one with the coins you have.

During odd moments of apparent boredom, I try to play with 24. On another note, I have never understood how people get bored.  There are so many places the mind can wander during silent moments.

  1. You can pay attention to the way you breathe which might lead you to notice a pattern but you may also wonder if such a pattern does exist in the absence of your attention or if it is induced by it. Then you get horrified because you realize that you will never know if a pattern exists or not unless someone else observes but can you trust someone else’s observation?
  2. You are alone in your room on a hot summer afternoon and the fan is on. It makes a distinct uniform sound as the blades move.  Some people call this noise.  Is it really noise?  You reason out that uniform sound of any kind cannot be called noise. The latter is a form of sound that serves as a source of annoyance.  If sound is uniform in the sense that it does not increase or decrease in intensity over time and is well within permissible levels, our mind can treat it like silence.  That way you can focus on one thing without getting distracted. Let me justify this by including a personal experience.  You are sitting in your balcony reading a book and you realize it is raining only when it switches from a drizzle to somewhat heavier downpour.  Your mind dwells on it for a few seconds but the realization that it is raining has not completely sunk it.  Once again you are jolted back into reality when it turns into a heavy downpour. This is when you realize that it is indeed raining.  Your mother is disappointed to see that you did not remove the clothes that were hung outside to dry. She blames it on your absent-mindedness but can you really call it that?  I would rather call it single-mindedness.
  3. Once I decided to work out 2 raised to 24 while I was waiting for food at a restaurant. I started with 2^5;32; 64;  128;  (125*2=250+6=256);  500+121000+242000+484000+96;   (200-8)+8000=8192;   (400-16)+16000 which is easier done if I take 100-16 = 84 then make it 384 after which it becomes 16,384. 350*2 is 700 which is added to 34*2(3*2=6 and 4*2=8) to make it 768 and finally 32,768.

1500 + (18*2) is 1536 where 536 is added to 65000 to make it 65,536.  You then move on to 131000 + 72 which is 131072 and from there you move to 260,000 + 2144 which is 262, 144.  By this time you know that it is easier to find solutions whereby you can just magically stitch the numbers together.

When I was new at playing with numbers I would approach 65,536 in a different way.  32,768 to 65,536 would have been 64000+1400+100+36 but over time you tend to skip steps because you become familiar with numbers.  They are no longer strangers to you so when you encounter a 768 you know it needs to become a 1500 and a 36.

Moving on from 262, 144 you encounter 520,000 and 4288 = 524,288.  This is what I meant by magically stitching numbers by first coming up with two numbers, such as 520,000 and 4288 and then knocking out the zeros.  In this case four zeros have been replaced by 4288 to make it 524,288. Congratulations. You just stitched two numbers. 

It is getting exciting because I am close to the number I have been waiting for.


Since 24 is easy to deal with, 524 000 becomes 1,048,000. I encounter 24 again because I have to double 12 (300-288) and then do 600 – 24 = 576; 1,048,576.  My mind is racing at this moment because I just finished that sum faster than any step before; since 24 is the most familiar number to me.

I use a multiple of 24 in the next step since I have to subtract 48 from 200 and add it to 1000 to make it 1,152(double of 576) and I add 2,097,000 to 152; arriving at 2,097,152.

Using a multiple of 24 in the next step would be senseless because I do not want to subtract 96 (i.e. 48*2) from 400 and reach 304.  I could instead do (150*2+4) and reach 304 which I can add to 4,194,000 to get 4,194,304.  In the next step I do 400 – 12 which is 388; hence 8,388,608.  One more step is left to reach 2 raised to 24.


I can use 24 again.

I can do 800-24 (double each number of my previous subtraction of 400-12 to get 776 but since I am dealing with 608 I need to arrange the numbers as follows: 777 and 216 instead of 776 and 1216 (608*2).  This gives me 16,000,000+777,000+216 = 16,777,216.

Needless to say, I had a cold lunch that day.




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