Deadline – 22nd of March!
Draw a square and choose four numbers to put at each vertex. For example:
Now in the middle of each segment write the positive difference between the two numbers at each end. e.g. the difference between 5 and 6 is 1.
Join these new points up with a square
Now in the middle of each segment of the new square find the positive difference of the numbers at each end. For example the difference between 15 and 1 is 14. Do this for all the segments and draw another square joining up your four new answers.
Keep finding the positive differences and joining these points up into a square until you reach 0,0,0,0.
Choose four new starting numbers and follow the instructions above to create your own version of this.
Our first choice of four starting numbers meant drawing 4 squares before we reached 0,0,0,0. How many squares have you drawn with your choice of starting numbers?
Your challenge is now to find the longest sequence of squares you can before the sequence reaches 0,0,0,0 and send us your answer.
An easy way to send sequences would be as lists of numbers. For example the one above could be written as
Please write giving us your longest sequence and any other thoughts on the puzzle using the “Leave a comment” button below.
I am Mr Meema Cyrus, a teacher at Mpesa foundation academy and I am so excited about my students collaborating with students at Lycee Francais’. I am looking forward to all your active participation.
Thanks for your message Mr Cyrus, we are starting the puzzle this lunch time and are looking forward to working with you, Mrs Fleming
Hi Cyrus,
My name is Okello Denis Omondi the former student at St, Aloysius but now working on this project. Am really glad on how active your students are. please keep it up.
thank you
Here is the longest sequence I found
3,12,7,10
7,9,5,3
2,4,2,4
2,2,2,2
0,0,0,0
Here is my longest sequence:
3,9,27,81
6,18,54,78
12,36,24,72
60,24,12,48
12,36,12,36
24,24,24,24
0,0,0,0
Hi Alex,
wow!! This is great Alex. I know mine might not be longer than yours. keep up the nice work you are doing.
Hey!
I did 7 with these 4 numbers:
1, 21, 15 and 63.
Thanks! Could you show all the steps of your sequence?
hi, fantastic app .
this is my longest sequence;
15 39 72 93
24 33 21 78
54 9 12 57
45 3 45 3
42 42 42 42
0 0 0 0
My longest sequence is:
9,13,16,4
4,3,12,5
1,9,7,1
8,2,6,0
6,4,6,8
2,2,2,2
0,0,0,0
that’s what i found:
83 2 1 12
81 1 11 71
80 10 60 10
70 50 50 70
20 0 20 0
20 20 20 20
0 0 0 0
My longest sequence is:
9898,6565,2121,7676
3333,4444,5555,2222
1111,1111,3333,1111
0000,2222,2222,0000
2222,0000,2222,0000
2222,2222,2222,2222
0000,0000,0000,0000
My longest sequence is
33,47,65,80
47,14,18,15
33,4,3,32
1,29,1,29
20,20,20,20
0,0,0,0
Here’s what we found
9000,6,1,5
8994,5,4,8995
8989,1,8991,1
8988,8988,8990,8990
0,2,0,2
2,2,2,2
0,0,0,0
Here is the formula you can use on geogebra or excel to find the positive difference between two numbers:
ABS(cell 1- cell 2)
Geogebra is a free piece of software you can use to explore many maths problems. It has a geometry view, and also a spreadsheet view.
You can use it online here. Just click on Spreadsheet on the right, and then try using the formula Alexi has given. You start off with an equal sign and the cells (boxes) have names like A1, B1 etc.
Try
=ABS(A1 – B1)
after putting two different numbers in A1 and B1.
If you get stuck, have a look at this one I have made
I have started using decimal numbers and fractions. This is the longest sequence I have come up with so far using this new method:
1.199999989, 2.22211E-05, 1E-04,5.0029912
1.199977768, 7.77789E-05, 5.0028912, 3.802991211
1.199899989, 5.002813421, 1.199899989, 2.603013443
3.802913432, 3.802913432, 1.403113454, 1.403113454
0, 2.399799978, 2.22045E-16, 2.399799978
2.399799978, 2.399799978, 2.399799978, 2.399799978
4.44089E-16, 0, 0, 4.44089E-16
4.44089E-16, 0, 4.44089E-16,0
4.44089E-16, 4.44089E-16, 4.44089E-16, 4.44089E-16
0, 0, 0, 0
Has anyone tried using numbers like square roots or fractions? Or even pi?!
I am peter-M-pesa Foundation Academy and i have tried many different numbers and i realized that one can only make a maximum of ten complete squares despite the numbers you use.
One of my answers was;
10,100,1000,10000
90,9900,9000,990
9810,900,8010,900
8910,7110,7110,8910
0,1800,0,1800
0,0,0,0