Let’s play game. Think of one number from 1 to 31 then see which table below has the number you think of.

16 | 17 | 18 | 19 | 8 | 9 | 10 | 11 | 2 | 3 | 6 | 7 | 1 | 3 | 5 | 7 | |||

20 | 21 | 22 | 23 | 12 | 13 | 14 | 15 | 10 | 11 | 14 | 15 | 9 | 11 | 13 | 15 | |||

24 | 25 | 26 | 27 | 20 | 21 | 22 | 23 | 18 | 19 | 22 | 23 | 17 | 19 | 21 | 23 | |||

28 | 29 | 30 | 31 | 28 | 29 | 30 | 31 | 26 | 27 | 30 | 31 | 25 | 27 | 29 | 31 |

The most left hand side table is table 1 and have weight 16. Next table 2 and have weight 8. Next table 3 and have weight 2. And the last, table 4 and have weight 1. For example, if you see you number at table 1 and 3, your number equals to weight at table 1 (1) + weight at table 3 (8) which is 9. Pretty simple isn’t it!! 😀

It’s not magic and we are using binary number to make it possible. In this example, we use 4 bit binary number. Table 4 which is the least significant number correspond to the weight 1 (2^{0}), table 3 correspond to 2 (2^{1}), table 2 correspond to 8 (2^{3}), and the last is table 1 which is the most significant number correspond to the weight 16 (2^{4}). In this example, we are not using numbers which have 1 bit on the 3^{rd} bit which correspond to 2^{2}.

For example, if your guessed number is at table 1 and 3, those tables corresponds to weight 2^{1} and 2^{4}. It means that those number in binary have 1 at the 2^{nd} and the 4^{th} bit, the rest are 0. So, your guessed number will be in the binary: 10010. If we want to make it to decimal, we have to multiply each binary digit with it’s corresponding weight. The decimal number will be 1*2^{4} + 0*2^{3 }+ 0*2^{2} + 1*2^{1 }+ 0*2^{0} = 17. So, your guessed number must be 17.

We are very lucky that we know binary number so we can put the number in 2-Dimensional table which looks very simple to play this game. If we only know decimal number, we must put one digit in decimal number to one 10-Dimensionl table which is impossible to see without help of computer. Let’s say if you want to play guessing number with 4 digit decimal number with help of decimal number, you must use four 10D tables which is super confusing.

I’m so amazed that this simple theory about binary number, with a little modification, can be applicable to make this “magic” game. Have fun!