Tutorial for Letter Puzzles

The idea of letter puzzles is a bit complicated, so here is a tutorial that shows you one way to solve the more difficult puzzles using organized charts!

1. Make a chart as shown:

1

2

3

4

5

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7

8

9

10

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12

A

B

C

D

J

Q

The idea is that all the letters that you have to solve for are listed on the left side. All the numbers that they might be are on top. As you figure out more information, you can put an X or a check to tell yourself that the letter doesn't equal or does equal the number. Ex. An X that is in line with D and 5 would mean that D can't be 5.

2. A strategy is always necessary to solve these puzzles. First, let's try to figure out (if we can) which letter is 1. Which letters are never the sum in an addition question and never the first letter in a subtraction question?

STATEMENT

POSSIBILITIES AND WHY

Q + Q = J

A B C D J Q, but it can't be J because Q is smaller than J.

A - Q = J

A B C D Q, but not A because J and Q must be smaller than A.

B + B = C

B C D Q, but not C because B is smaller than C.

C - D = A

B D Q, nothing else can be known.

B - A = A

B D Q, but it can't be B because A is smaller than B.

After all that

D and Q could both be 1. We should put that in the chart soon, and try this again after we know more information.

3. Writing down all the facts of which letters are larger than others is also useful. Note that you could do this step without doing step 2, which may save time depending on your strategy.

Q < J and J is an even number, because J = Q + Q. If Q is an odd number, or an even number, Q + Q = even #.
A > J meaning A is greater than 1, and because J is greater than Q, A must be greater than 2 (If Q = 1, J would =
2, then A could equal 3 - but A can't be any lower than 3.)
A > Q because J is greater than Q, and A is greater than J.
C > B, and C is an even number.
C > D
B > A , and B is an even number.
C > B > A > J > Q and since C > D, C is the highest number! C MUST equal 12!

4. For each even number, all the odd numbers for that letter can be crossed out as shown below.
5. For every time a letter is smaller than another letter, cross out its highest possibility. Ex. Q < J, so Q can't be 12. It is also smaller than A, so it can't be 11, etc.
{The chart below is colour coded according to the text from step 4+, so that you can see why each X is there.}
Also note that since we know C does equal 12, all the other possibilities of 12 can also be crossed out.
In 'A', since B is larger than A, A can't be 11. In fact, A has to be half of B! If, in the most extreme case, B is 10, A has to be 5. The highest possibility at the moment is that A is 5 or less. The vice versa goes for B, since B must be twice as much as A, and A can't be 1 or 2 (A is greater than at least two other letters), B can't be 2 or 4.
Note that C - D = A. If D = 1, then C - D = A would mean 12 - 1 = 11 - but A can't be 11! Therefore D can't be 1. Same thing for D being 2 through 6. It just can't be.
Now, look! There is only one available spot left for 1. Q must equal 1, since the "Low" and the "High" must have a letter equal to them! I explain this more below the chart.

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A

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B

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C

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C = 12

D

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J

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Q

Q = 1

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X

6. The logic above could go on until the whole puzzle was finished, and you will likely do that for most puzzles. Before we do that, you need to know a few facts. Note that there are 12 available number spots, while only 6 letters. This means that, as shown above, just because numbers 3 and 5 look like A has to be that number, it doesn't . Since there are wholes, you can't know for sure that A equals 3 or 5. J may equal 2, or no letter may equal 2. This is important to understand, otherwise you'll run into problems.

7. Above, B + B = C. This means B is half of C, which is 6! Since we know that C must equal 12, we know that B has to equal 6. Even if we didn't, we could prove that it wasn't 7 or above because the highest number is 12, therefore half of 12 is 6, lower than 7.

8. The opposite logic from step 7 can be applied in this way: Since Q + Q = J, without knowing what Q equals, we know that J can't equal 1 because Q is smaller than J and 1 is the smallest number! In this case, we know what Q equals.

B - A = A OR half of 6 is A or A = 3
C - D = A OR 12 - D = 3 meaning 12 - 3 = D or D = 9
Q + Q = J OR 1 + 1 = J OR J = 2

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12

A

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X

A = 3

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B

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B = 6

X

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C

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C = 12

D

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D = 9

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J

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J = 2

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Q

Q = 1

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X

If you were doing this for a high-score puzzle, you may wish to check your answer by substituting all your letters back into the original equations. Ex.

Since we know that 3 - 1 does infact equal 2, we know that "A - Q = J" is also a true statement. For all our answers to be correct, all the equations in the puzzle must be true. So, if you run into an equation that isn't true, there is either a problem with your answers, or - if you've re-checked thousands of times, it is possible that you have found a real IMPOSSIBLE MATH PUZZLE - and you should email me with your discovery, since I may have made a mistake. You may use the Answer Submitter for that purpose if you wish.

STATEMENT	POSSIBILITIES AND WHY
Q + Q = J	A B C D J Q, but it can't be J because Q is smaller than J.
A - Q = J	A B C D Q, but not A because J and Q must be smaller than A.
B + B = C	B C D Q, but not C because B is smaller than C.
C - D = A	B D Q, nothing else can be known.
B - A = A	B D Q, but it can't be B because A is smaller than B.
After all that	D and Q could both be 1. We should put that in the chart soon, and try this again after we know more information.