8 0 -4 -7 5 5 -11 11
14 -11 3 9 -4 -13 14 1
2 1 7 -6 14 -3 -3 3
12 -10 -14 12 -11 10 -4 -4
-13 -11 8 -12 1 14 3 -12
-1 -3 2 2 4 -10 -8 -5
-9 2 11 11 -10 5 -10 -12
[/code]
Your task is to pick elements out of this
array so that the sum of the elements you
pick is as large as possible. You may
pick the same element multiple times as
long as you don't violate any of the
following rules. Also, in the following,
"between" is always inclusive.
OVERALL RULE:
You must choose precisely 100 elements
out of the array.
ROW RULES:
You must choose between 4 and 30 elements
from the first row, between 7 and 39 from
the second row, between 8 and 20 from the
third, between 6 and 22 from the fourth,
between 7 and 35 from the fifth, between
4 and 29 from the sixth, and between 2
and 47 from the seventh.
COLUMN RULES:
You must choose between 1 and 31 from the
first column, between 3 and 42 from the
second, between 7 and 36 from the third,
between 7 and 40 from the fourth, between
5 and 30 from the fifth, between 1 and 34
from the sixth, between 1 and 9 from the
seventh, and between 3 and 38 from the
eight.
INDIVIDUAL ELEMENT RULES:
In the following array, the element [A,B]
in the i[sup]th[/sup] row and j[sup]th[/sup] column specifies
that you must choose the element located
in the i[sup]th[/sup] row and j[sup]th[/sup] column of the
original array between A and B times.
Question
superprismatic
Consider the following array of numbers:
So, for example, the -7 in the first
row of the original array must be chosen at
least twice but no more than 9 times.
I have checked several times that it is possible to
make choices which follow all the rules. I have a
putative best answer. See how large your sum of
100 elements can be while following all the rules.
I'll let you know if you get close (or surpass) my
best answer.
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