If you take a lot of numbers and then square them and them subtract the result of each number from the one above it you will notice a pattern.
1²=1 4-1=3
2²=4 9-4=5
3²=9 16-9=7
4²=16 25-16=9
5²=25 36-25=11
6²=36 49-36=13
7²=49 64-49=15
8²=64 81-64=17
9²=81 100-81=19
10²=100
Every time the number you are going up by is increasing by 2. That phrase sounds a lot like my last post. So, let's see if there's something similar for the cubes.
1³=1 8-1=7
2³=8 27-8=19
3³=27 64-27=37
4³=64 125-64=61
5³=125 216-125=91
6³=216 343-216=127
7³=343 512-343=169
8³=512 729-512=217
9³=729 1,000-729=271
10³=1,000
This looks a lot like the exponents from before, except different numbers. So maybe we need to do it again?
19-7=12 127-91=36
37-19=18 169-127=42
61-37=24 217-169=48
91-61=30 271-217=54
It worked! We have the numbers which are increasing by a number again. The difference is that this time it's 6. So it's probably either going up by 4 or multiplying by 3. I'll do one more to see, though I'll probably have to subtract 3 times this time.
14=1 16-1=15 65-15=40 110-40=70 84-70=14
24=16 81-16=65 175-65=110 194-110=84 108-84=20
34=81 256-81=175 369-175=194 302-194=108 132-108=24
44=256 625-256=369 671-369=302 434-302=132 156-132=24
54=625 1,296-625=671 1,105-671=434 590-434=156 180-156=24
64=1,296 2,401-1,296=1,105 1,695-1,105=590 770-590=180 204-180=24
74=2,401 4,096-2,401=1,695 2,465-1,695=770 974-770=204
84=4,096 6,561-4,096=2,465 3,439-2,465=974
94=6,561 10,000-6,561=3,439
104=10,000
Well, I had to do 4 subtractions instead of the 3 I anticipated and something unexpected happened. After 2 numbers it got stuck in a rut of 24. I'll see what happens if I add the 11th number.
114=14,641. 14,641-10,000=4,641. 4,641-3,439=1,202. 1,202-974=228. 228-204=24!
Well, I think it's broken. If you want to do the next stage, do it, but since it might be 8 subtractions, it will be a lot of work. I'm not going to do it, but if you do, please post your findings in a comment for this post.
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