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## Here's an example of a simple Equatum puzzle:

There's a grid which looks like a crossword.

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.

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