# Re: Good one to keep Joel off the streets...

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Posted by Joel on October 11, 2002 at 10:44:58:

In Reply to: Good one to keep Joel off the streets... posted by Denis Borris on October 09, 2002 at 16:08:08:

: a+b+c+d+e+f = g+h+i+j+k+l

: a^2+b^2+c^2+d^2+e^2+f^2 = g^2+h^2+i^2+j^2+k^2+l^2

: a^3+b^3+c^3+d^3+e^3+f^3 = g^3+h^3+i^3+j^3+k^3+l^3
: ...repeat for ^4 and ^5

: All 12 numbers are different, greater than 0 and under 25.

: Nice looper for you to program, Joel !

: since 24^12 = 36,520,347,436,056,576 lotsa shortcuts required.
: At 1 second each: 24^12 / 365*24*60*60 = 1,158,052,620 years :)

OK - before I even start this we have to clarify the question. The way you wrote it, it sounds like you are looking for a single set {a,b,c...l} such that
a+b+c+d+e+f = g+h+i+j+k+l
AND
a^2+b^2+c^2+d^2+e^2+f^2 = g^2+h^2+i^2+j^2+k^2+l^2
AND
a^3+b^3+c^3+d^3+e^3+f^3 = g^3+h^3+i^3+j^3+k^3+l^3
AND
a^4+b^4+c^4+d^4+e^4+f^4 = g^4+h^4+i^4+j^4+k^4+l^4
AND
a^5+b^5+c^5+d^5+e^5+f^5 = g^5+h^5+i^5+j^5+k^5+l^5

Well, I don't know how to prove it abstractly, but I'm pretty sure that set is {}; i.e. it don't exist.

So, maybe you are asking for a program that will find ALL sets {an, bn, cn, dn, en, fn, gn, hn, in, jn, kn, ln} such that
an + bn + cn + dn + en + fn = gn + hn + in + jn + kn + ln

AND
ALL sets {ao, bo, co, do, eo, fo, go, ho, io, jo, ko, lo} such that
ao2 + bo2 + co2 + do2 + eo2 + fo2 = go2 + ho2 + io2 + jo2 + ko2 + lo2

and so on, up to ALL SETS {as, bs, cs, ds, es, fs, gs, hs, is, js, ks, ls} for which
as5 + bs5 + cs5 + ds5 + es5 + fs5 = gs5 + hs5 + is5 + js5 + ks5 + ls5

Many different sets.

Is THAT what you're looking for?

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