Plz help me? math questions?

Posted on 2016-04-06 19:06:00 in Math by JACK DASON

Q7. Opposite corners :This is an exploration/investigation question 
Here consecutive numbers are arranged in 7 columns. You can add as many rows as you like. 

1 2 3 4 5 6 7 
8 9 10 11 12 13 14 
15 16 17 18 19 20 21 
22 23 24 25 26 27 28 
29 30 31 32 33 34 35 
36 37 38 39 40 41 42 
43 44 45 46 47 48 49 
50 51 52 53 54 55 56 
57 58 59 60 61 62 63 

In the 2 by 2 square below notice that 
5 6 
12 13 

5×13=65and12×6=72 and the difference between them is 7. 

In the 3 by 3 square below, look at the opposite corners and notice that 
10 11 12 
17 18 19 
24 25 26 

10×26=260 and 12×24=288 and the difference between them is 28. 

a) Investigate to see if you can find any rules or patterns connecting the size of the square chosen and the difference.

b) Test your rule by looking at squares of the size 4 by 4 or 5 by 5 or larger. Try at least two examples. 



c) Can you write down a rule for arrays arranged in 8 columns? 



d) Can you generalise the rule to arrays arranged in n columns? 


e) Can you prove the rule found in d)?

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