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Free printable Anagram magic square with answers

An anagram magic square is a word puzzle and a number puzzle in the same grid. Every box holds a five-letter word. Every entry in the numbered list beside it is a six-letter word that uses all five of one box’s letters plus one more. Write each entry’s number in its box, and the numbers come out a magic square: every row, column and diagonal adding to the same total. Then read the letters you added, in entry order, and they spell a saying.

By size

A grade is the grid, from a 3 by 3 up to a 6 by 6, which is also how many letters the hidden saying has. The bigger grades add entries that share four of some box’s five letters, so you count rather than recognise, and the top two leave a box the letters cannot settle on their own.

By audience

It is the puzzle for solvers who like words but miss having something to add up: the letters get you most of the way and the arithmetic finishes the grid.

One answer, and two ways to check it

Every puzzle is proved before it prints: a solver searches every way the LETTERS allow the entries to be placed, and every way the row, column and diagonal sums allow it, and the puzzle only ships if exactly one arrangement survives both. That is also where the difficulty comes from, because the two checks come apart. On the easy and medium grades the letters settle every box on their own and the sums are just a way to catch a mistake. From the hard grade up we plant a box that genuinely fits two entries, and measured what that does: the letters alone leave two arrangements open at hard and extreme, and four at evil, and the line sums bring every one of them back to a single answer. Swapping two numbers in a magic square always breaks a line, which is why the arithmetic can always decide what the letters cannot. The hidden saying is the third check, and the one you will actually use: a wrong match shows up as a saying that stops reading.

How to solve an anagram magic square

Every box holds a five-letter word, and every entry in the numbered list is a six-letter word that uses all five of one box’s letters plus one more. Write each entry’s number in its box; the numbers come out a magic square, and the letters you added spell a saying.

The method

  1. 1Work from the list, not the grid. Take entry one and ask which box’s five letters are all inside it. That is a smaller question than looking at a box and wondering which of twenty-five entries might fit, and it is the same question twenty-five times, which is what makes the puzzle move.
  2. 2Check the fifth letter, not the first four. Most wrong matches share four of the five. STONE is in STONES and it is not in STORED, and the only way to tell is to account for every letter rather than recognising the shape of the word. On the harder grades there are sixty of these near-misses on one page, which is most of the work.
  3. 3Write the added letter down as you go. Beside entry one, write the letter the entry has that its box does not. Do it while the comparison is in front of you rather than at the end. Those letters, read in entry order, spell a saying, and a wrong match shows up as a saying that stops reading, which is the best check you have.
  4. 4Let the sums finish it. From the hard grade up, one box genuinely fits two entries and the letters cannot choose. Look at the row and the column it sits in: only one of the two numbers lets both reach the target, because swapping two numbers in a magic square always breaks a line. That is the step the arithmetic is there for.
The one rule people get wrong
The letters of the box need not appear in the entry in order: they are an anagram, not a prefix. ONSET is five of the six letters of STONES just as much as STONE is. Sort the letters if it helps.
What the answer page shows
The same grid with every number written in, and the saying printed under the word list, so you can check the letters you collected against it.
How the grades differ
The grid, from a 3 by 3 up to a 6 by 6, which is also how long the hidden saying is. The harder grades add near-misses on purpose, and the top two leave a box the letters cannot settle.
Do the sums matter on the easy grades?
They are a check rather than a step. On easy and medium the letters settle every box on their own, so the magic square is how you find a mistake. From hard up it is doing real work: we measured it, and the letters alone leave two arrangements open at hard and four at evil.
Is it the same as a magic square?
It contains one. A plain magic square is arithmetic only, and you are given some of the numbers; here you are given none of them, and the words are what tell you where each number goes.
Good for
Anyone who likes word puzzles but misses having something to add up.

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