How to solve alphametic puzzles

I recommend reading this before watching the video… There are key elements to solving most alphametics.

• 在许多情况下，附加问题的结果是一位数字更长(in digit-length) than the addends – the numbers added. If there are only two addends, this implies that the extra digit is the number 1.

让我们看一个非常简单的字母：我+我=蜜蜂

The letter Bmustrepresent the digit 1, since when you add two 2-digit numbers you cannot possibly get a number larger than 198. That happens when both addends are 99. Since M and E are two different numbers, they will certainly be even smaller than 99! In any case, the hundreds digit in the sum, represented by B in our example, must be 1.

• In two addend alphametics, there may be columns that have the same letter in both the addends and the result. If such a column is the units column, that letter must be 0. Otherwise, it can either be 0 or 9 (and then there is a carry).

In the alphametic: ME+ME=BEE the column of the unit’s digits is: E+E=E There is only one digit, which has the property that when you add it to itself you get the same digit as the result – zero! Only the sum of two zeros is zero, so E must be equal to 0.

The solution to this alphametic is therefore: B=1, E=0, M=5: 50+50=100.

Here are some tips for solving more complicated alphametics.

• If there are more than 2 addends, the same rules apply but need to be adjusted to accommodate other possibilities. If there are four identical letters in the units column (one of them the sum), this letter can now be: 0 or 5 (because 5+5+5=15). If there are four identical letters in a different column (one of them the sum), this letter can now be: 0 or 5 (no carry), 4 or 9 (carry 2). Four identical letters in a column other than the units column means a 1 could not have been carried over (why not?). This rule can be worked out for more than 3 addends as well…
• It is wise to turn subtraction problems into addition problems by adding the result to the smaller addend to get the larger one.
• 面对一些字母的选项时，请尝试一个，直到您获得正确的答案或找到矛盾为止。

Now let’s look at a slightly more advanced cryptarithm. This video shows how to solve the alphametic: NO + GUN + NO = HUNT. Note the ‘neat’ sentence: “No gun, no hunt!”.