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Fun With Num3ers | Just another WordPress.com site
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Fun With Num3ers | Just another WordPress.com site
Just another WordPress.com site
Partitioning| (x+y+z)^4 – (y+z)^4 – (z+x)^4 – (x+y)^4 + x^4 + y^4 + z^4 | Fun With Num3ers
Consider the identity: $latex (x+y+z)^4 - (y+z)^4 - (z+x)^4 - (x+y)^4 + x^4 + y^4 + z^4 = 12 \; x \; y \; z \; (x+y+z)$ 118 can be partitioned into three parts that have the same product in 4 ...
Sums & Products| x+y+z=a+b+c and x*y*z=a*b*c | Fun With Num3ers
Note that 118 can be partitioned into three parts that have the same product in 4 different ways: $latex 14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118$ and $latex 14 \times 50 ...