First calculate 999...999 ^ 2:
The base number itself is one less than 10^2000, so the square will be almost 10^4000. From the pattern set by
999^2 = 998001
9999^2 = 99980001
99999^2 = 9999800001
...
the square will have 1999 9's, an 8, 1999 zeros and a 1, in that order.
But we can go directly to the pattern of the cubes:
n n^3
9 729
99 970299
999 997002999
9999 999700029999
99999 999970000299999
With n consisting of 2000 9's, the cube would involve 1999 9's followed by a 7, then 1999 zeros and a 2 and finally 2000 9's.
So the desired s.o.d. is 1999*9 + 7 + 2 + 2000*9 = 36,000.
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Posted by Charlie
on 2019-04-15 19:47:46 |
solution
