January/February 2007: The Sixteen Grid

Each of the numbers 1, 2, …, 16 is used exactly once in the empty cells to form arithmetic expressions connected by symbols for the four basic operations. Each row (column) is an arithmetic expression, read and performed left to right (top to bottom), disregarding the usual order of operations, to yield the result at the right (bottom).

Hints

Before you begin, here’s a good clue,
Beware of the list, for one is untrue.

To get a start, with vim and vigor,
See that the top right number couldn't possibly be bigger.

For another corner, you must reject
Any and all numbers that are not perfect.

Stumped? Don't fall into depression:
The first three entries in one row are in geometric progression.

For salvation don't look to the gods or run for the border,
One row is consecutive odds (though not in order).

If you are really stuck, can linear algebra cure your anxiety?
The puzzle complete has determinant -15090

Now, buster, before you tire of reading these rhymes
No row or column has more than two primes.

When you solve this you'll feel like a hero,
Three numbers in one column, in one base, end in zero.

Puzzle was originally posted by the American Mathematical Society.