Here's an example of a simple Equatum puzzle:

There's a grid which looks like a crossword.

5x5 grid.png

Clues

ACROSS
1    Arrange 189 + =
4    Arrange 123 + =
5    Arrange 257 + =

 

DOWN
1    Arrange 358 + =
2    Arrange 112 + =
3    Arrange 279 + =

And there's a list of clues, each of which gives the numbers and operators which are arranged to form an equation which is written in the grid.

What is an Equatum?

When we learn arithmetic, we solve equations like: 2+3=? where the ? represents a number.
 

If we go on to learn algebra then we solve equations like: 12+?=5 where again the ? represents a number. We might solve some puzzles such as: 5?2?4=28 where this time the ?s represent operators: + – x ÷.
 

In all the above, either the unknowns are numbers or they are operators but we always know whether we are looking for a number or an operator.

The new term "Equatum" is used to describe a problem where for at least one of the unknowns, we don't know in advance whether we are looking for a number or an operator or an equals - it could be any of these!

So to give a simple example we could have the problem:  51=3??7 where the ?s can be any of the following symbols: 0 1 2 3 4 5 6 7 8 9 + – x ÷ =.  Can you find the solution?

The only solution is: 51=3x17.

Or what about:  61=5??7.  Can you find the solution?

The only solution is: 61=54+7.

Another type of Equatum would be where we are given all the symbols but we don't know what order they go in.
 

Here's an example of this type of Equatum: "Arrange 1257+=".
This has four possible solutions.  See if you can find them...

There are four possible solutions: 5+7=12, 7+5=12, 12=5+7, 12=7+5.

The "Equatum Puzzles" book fills crossword-like grids with this type of problem.