Strange Squares
10 07 2007
Look at the green square which contains the numbers 2, 3, 12 and 13.
What is the sum of the numbers that are diagonally opposite each other?
Do you notice anything?
Have a look at other squares on this grid and leave a comment on your findings.
Click here to download your own 100 square to print off and investigate.
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Andrew here!
I found out with these squares that it works all the time you try it!
Even with rectangles it works. Although it dose not work with a square sort of thing with a 2 number space gap at the top and 2 number spaces at the bottem there is no gap between two numbers.
This is Andrew reporting back!
I found out that if you do a sqaure or a rectangle you will still end up with the same number each time you do it diagonally and that you can do it like ten by ten.
i discovered that you have to change the digits around with the tens. for example, 43 + 34 = 77, and 33 + 44 = 77. I also discovered that the two numbers always add up to the same number
1. green square
they both add up to 15 and the pink square diagonally add up to 47 like 18+29 and 19+ 28. Also all the squares are odd +even except the blue and the red where its odd + odd. this toime there is a two numer difference between the sums.Every time theanswers in the same squares add up to the same like with the green its 15 and with pink its 47 and so on.
I noticed that the same thing happened because they are odd and even.
75+86=161
76+85=161
I found out that when the square is highlighted there is always a square that is highlighted underneath and it always uends up with the same answer
Edward
Why?
2 and 3 are 10 less than 12 and 13. This means that the numbers have something in common, adding up to the same answer. 2 and 3 makes 5, because 12 and 13 have a ten infront of them 5 becomes 15.
Joe
Why?
This happens because you take 1\2\3 off and add 1\2\3 on e.g. 3 + 12 - 1 from 3 = 2 and + 1 to 12 = 13. So basicly you take away 1and add 1.
Green squares
The units are the same in two squares each (2 and 3) so they both add up to 15
Blue squares
Both opposite diagonals have a 2,1,5,4 in the numbers
Why
A times table runs down every column of the grid. A number underneath another in the same column will have the same unit. A row running horazontally will have the same ten rather than the unit, so there will always be the same four didgets in four numbers.
the green squares both add up to 15 like he pink square and all the others. All the square odd + even except for the red and blue which adds odd and odd.