Let’s play a game
Our Game - Pick a number Pick a number 1 to 31 and tell me in which columns your number is present in the grid. Be careful to check all columns. Example – No. 23 is in cols 1, 3, 4 & 5. Let’s try a few before we see how it’s done.
Col 1 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Col 2 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31
Col 3 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 31
Col 4 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 31
Col 5 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
A Simpler Version Only 4 columns here Can you spot the trick now? Pick a number 1 to 15 and tell me in which columns your number is present in the grid. Any offers before we move on?
Col 1 8 9 10 11 12 13 14 15
Col 2 4 5 6 7 12 13 14 15
Col 3 2 3 6 7 10 11 14 15
Col 4 1 3 5 7 9 11 13 15
Even Simpler? Can you spot the trick now? Pick a number 1 to 15 Tell me the no. at the top of each column where your number is present. Any offers before we move on?
8 9 10 11 12 13 14 15
4 5 6 7 12 13 14 15
2 3 6 7 10 11 14 15
1 3 5 7 9 11 13 15
So how is it done? So this is how the game is played:Pick a number -
6
At the top of the cols where 6 is present we have 4 & 2. 4+2=6 But will you impress your friends with this? A 5 column game is more impressive.
8 9 10 11 12 13 14 15
4 5
2 3
6
6
7 12 13 14 15
7 10 11 14 15
1 3 5 7 9 11 13 15
Play the game again Looking at the top two rows we see: Col Col Col Col Col 1 16
Pick a number -
2 8
3 4
4 2
5 1
?
? is in cols 1, 3, 4 & 5. A bit of practice needed to remember the top row nos. 16 + 4 + 2 + 1 = 23 Will your friends be impressed? Game sheets available to try.
Col 1 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Col 2 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31
Col Col 3 4 4 2 5 3 6 6 7 7 12 10 13 11 14 14 15 15 20 18 21 19 22 22 23 23 28 26 29 27 30 30 31 31
Col 5 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Summary What have we done? All data in a computer system is held in binary. There are many different data types, numbers, text images, instructions, messages etc. We have just converted binary numbers to decimal numbers. How? That’s for another lesson