What Difference Does It Make-answer
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Challenge problem
02
02 12 22 32 42 52 62 72
12
22
32
42
52
62
72
0
1
4
9
16
25
36
49
X
0
3
8
15
24
35
48
X
X
0
5
12
21
32
45
X
X
X
0
7
16
27
40
X
X
X
X
0
9
20
33
X
X
X
X
X
0
11
24
X
X
X
X
X
X
0
13
X
X
X
X
X
X
X
0
First I started off by making a table. My table extended from 72 across to 72 down. I filled out the table by finding out the difference between the different squared numbers. I immediately noticed that every odd number works(is a difference between two squared numbers). I noticed this after looking at this:
02
02 12 22 32 42 52 62 72
12
22
32
42
52
62
72
0
1
4
9
16
25
36
49
X
0
3
8
15
24
35
48
X
X
0
5
12
21
32
45
X
X
X
0
7
16
27
40
X
X
X
X
0
9
20
33
X
X
X
X
X
0
11
24
X
X
X
X
X
X
0
13
X
X
X
X
X
X
X
0
I realized that because this diagonal row contains every odd number, then all odd numbers work. Now, I tried to look for patterns with the even numbers. I learned that all the even numbers that work are divisible by four. I tried out many ways to see the pattern with evens and finall figured out that: in order to check if an even number works, you divide it
by four(if it is not divisible by 4 then that number doesn’t work) and then pick the number one greater from it and one less that it. For example: The number = 16 16/4=4 (take the number 1 greater than it and 1 les than it) 4-1=3, and 4+1=5 So 52-42=16
02
02 12 22 32 42 52 62 72
12
22
32
42
52
62
72
0
1
4
9
16
25
36
49
X
0
3
8
15
24
35
48
X
X
0
5
12
21
32
45
X
X
X
0
7
16
27
40
X
X
X
X
0
9
20
33
X
X
X
X
X
0
11
24
X
X
X
X
X
X
0
13
X
X
X
X
X
X
X
0
First I started off by making a table. My table extended from 72 across to 72 down. I filled out the table by finding out the difference between the different squared numbers. I immediately noticed that every odd number works(is a difference between two squared numbers). I noticed this after looking at this:
02
02 12 22 32 42 52 62 72
12
22
32
42
52
62
72
0
1
4
9
16
25
36
49
X
0
3
8
15
24
35
48
X
X
0
5
12
21
32
45
X
X
X
0
7
16
27
40
X
X
X
X
0
9
20
33
X
X
X
X
X
0
11
24
X
X
X
X
X
X
0
13
X
X
X
X
X
X
X
0
I realized that because this diagonal row contains every odd number, then all odd numbers work. Now, I tried to look for patterns with the even numbers. I learned that all the even numbers that work are divisible by four. I tried out many ways to see the pattern with evens and finall figured out that: in order to check if an even number works, you divide it
by four(if it is not divisible by 4 then that number doesn’t work) and then pick the number one greater from it and one less that it. For example: The number = 16 16/4=4 (take the number 1 greater than it and 1 les than it) 4-1=3, and 4+1=5 So 52-42=16
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