The coordinates at
the top of the page are not for the cache but are convenient for
parking.
One of Ben’s
favourite puzzles is Futoshiki, where
you are given a grid with > or <
operators associated with some of the
squares and have to fill in the squares with numbers which obey the
> and < operations in the rows and columns. This cache takes
that idea one step further.
In the grid below
there are the +. -, x , and / operators
separated by blank squares where you have to fill in numbers. You
must insert numbers, one digit per square, to get 13 valid
equations. Each calculation in a row proceeds from left to right in
a sequential manner rather than according to a division and
multiplication first system. For example
2+3+5-7/3-1=(2+3+5-7)/3-1 = 0 rather
than (2+3-5)-7/3-1 = 20/3.
In addition to the
row equations being correct, the sum of the digits in each of the
thirteen columns must add up to 40.
The numbers that
you can use for the calculation must be taken (once only) from the
following set
1, 1, 2, 2, 2, 4, 4, 4, 6, 6, 7, 7, 9
,9, 9, 9,
11, 12, 15, 17, 19, 19, 20, 21, 21, 25, 34, 38, 66, 74, 83, 87,
99,
141, 173, 204, 221, 241, 306, 682, 771,
3825, 3948, 5304, 7106, 9962,
10061, 13081, 18234, 35292, 36468, 52324, 82908
Once you have
solved the puzzle there follows a little algebra to augment the
arithmetic.
Let
A= Cell E7
B= Cell I11
C= Cell J3
D= Cell M13
E= Cell G3
F= Cell I5
The cache is
located
at
N 51 57.ABC W 000 00.DEF
You can check your answers for this puzzle on
Geochecker.com.