When you have a list of numbers and a target batch total to check it against, you can often spot a transposition error and narrow down the probable source.
Consider how travel expenses are processed. Say that every item you receive is accompanied by a paper receipt and is entered into a database. When you add the values on the receipts using a calculator, you get 133.56, but the database says the total is 131.76.
In Table 520, the "Correct values" column shows the numbers as they appear on paper; the "Incorrect values" column shows what has been entered into the database. Notice that the values are in pence or cents. Having a decimal point makes little difference, but it is neater to work with whole numbers. The challenge is to track down the transposition error where the value 1754 has been entered as 1574.
Correct values  Incorrect values (the column v)  

2460  2460  
1452  1452  
1450  1450  
1610  1610  
1772  1772  
1160  1160  
**Transposition error**  175 4  157 4 
1698  1698  
Total  13356  13176 
The difference in the totals is 180. The rule of thumb is this: when a batch totals error is a multiple of 9 the problem is likely to be a transposition error. In this case, the magnitude of the difference tells us that the transposition is between the hundreds column and the tens column (giving us 18). Further, because 18 / 9 = 2, you know that the digit difference is 2, and you are looking for 02, 13, 24, 35, 46, 57, 68, or 79 in those two columns of v. In this example, the column v total is lower than the correct total. If the total in column v had been higher than the other total you would be looking for 20, 31, 42, and so on.

The magnitude of the error gives you the column position and the digit difference helps find the pattern required. You can calculate these values using numbers as numbers or numbers as strings:
mysql> SET @correctTotal = 13356; Query OK, 0 rows affected (0.00 sec) mysql> SET @diff = (SELECT SUM(v) FROM incorrect)  @correctTotal; Query OK, 0 rows affected (0.00 sec) mysql> SET @magnitude = POWER(10,FLOOR(LN(ABS(@diff))/LN(10))1); Query OK, 0 rows affected (0.00 sec) mysql> SET @digitDiff = @diff/@magnitude/9; Query OK, 0 rows affected (0.00 sec) mysql> SELECT @diff, @magnitude, @digitDiff; ++++  @diff  @magnitude  @digitDiff  ++++  180.00  10  2  ++++

Using the magnitude, you can extract the two candidate digits from each number in the list. This query extracts the relevant pair of digits from each number in the batch, and it displays the digit difference:
mysql> SELECT v,FLOOR(v/@magnitude/10) % 10 AS digitA, > FLOOR(v/@magnitude) % 10 AS digitB, > FLOOR(v/@magnitude/10) % 10  FLOOR(v/@magnitude) % 10 > AS digitDiff > FROM incorrect; +++++  v  digitA  digitB  digitDiff  +++++  2460.00  4  6  2   1452.00  4  5  1   1450.00  4  5  1   1610.00  6  1  5   1772.00  7  7  0   1160.00  1  6  5   1574.00  5  7  2   1698.00  6  9  3  +++++
You are looking for a digit difference of 2 between columns digitA and digitB; if these columns are switched the result would account for the 180 error in the batch total. For example, if you switched the 4 and the 6 in the number 2,460 the result would be 180 more, and that's exactly what you need to get your totals to agree.
mysql> SELECT > v, > CASE WHEN FLOOR(v/@magnitude/10) % 10  > FLOOR(v/@magnitude) % 10=@digitDiff THEN '*******' > ELSE '' END > AS investigate > FROM incorrect; +++  v  investigate  +++  2460.00  *******   1452.00    1450.00    1610.00    1772.00    1160.00    1574.00  *******   1698.00   +++
You cannot tell which of the two marked values is responsible for the error; in fact, you cannot be certain that it was a transposition that caused the error. However, this tells you where to start your investigation.
5.15.1. SQL Server
The same code runs more or less unchanged in SQL Server. However, you must declare your variable as INTEGER and the logarithm function is called LOG, not LN:
DECLARE @correctTotal AS INTEGER DECLARE @diff AS INTEGER DECLARE @magnitude AS INTEGER DECLARE @digitDiff AS INTEGER SET @correctTotal = 13356 SET @diff = (SELECT SUM(v) FROM incorrect)  @correctTotal SET @magnitude = POWER(10,FLOOR(LOG(ABS(@diff))/LOG(10))1) SET @digitDiff = @diff/@magnitude/9 SELECT @correctTotal, @diff, @magnitude, @digitDiff; SELECT v,FLOOR(v/@magnitude/10) % 10 x,FLOOR(v/@magnitude) % 10 y FROM incorrect SELECT v, CASE WHEN FLOOR(v/@magnitude/10) % 10 FLOOR(v/@magnitude) % 10=@digitDiff THEN '*******' END investigate FROM incorrect; GO
5.15.2. Oracle
In Oracle, the method for setting and retrieving variables is slightly different. You can declare variables and assign them using the SELECT ... INTO statement from inside a BEGIN END block.
You use the MOD function in place of the % operator:
set serveroutput on DECLARE correctTotal NUMBER := 13356; diff NUMBER; magnitude NUMBER; digitDiff NUMBER; v NUMBER; id NUMBER; CURSOR mCursor IS SELECT t.v, 10 * t.x + t.y  (10 * t.y + t.x) id FROM (SELECT v, MOD(FLOOR(v/magnitude/10),10) x, MOD(FLOOR(v/magnitude), 10) y FROM incorrect) t WHERE 9*(xy) = diff/magnitude; a NUMBER; b NUMBER; BEGIN SELECT SUM(v) correctTotal INTO diff FROM incorrect; SELECT POWER(10,FLOOR(LN(ABS(diff))/LN(10))1) INTO magnitude FROM dual; SELECT diff/magnitude/9 INTO digitDiff FROM dual; dbms_output.put_line(correctTotal); dbms_output.put_line(diff); dbms_output.put_line(magnitude); dbms_output.put_line(digitDiff); OPEN mCursor; LOOP FETCH mCUrsor INTO a,b; EXIT WHEN mCUrsor%NOTFOUND; dbms_output.put_line(a); dbms_output.put_line(b); END LOOP; CLOSE mCursor; END; /
5.15.3. Single Query
Each example shown so far uses programming constructs, but these are really for convenience, they are not essential. You can run the entire process as a single SQL statement:
mysql> SELECT v, > CASE WHEN FLOOR(v/magnitude/10) % 10  > FLOOR(v/magnitude) % 10=digitDiff > THEN '*******' > ELSE '' END AS investigate > FROM incorrect CROSS JOIN > (SELECT batchTot, diff, magnitude, digitDiff > FROM > (SELECT > diff/magnitude/9 AS digitDiff, > magnitude,diff,batchTot > FROM > (SELECT > POWER(10,FLOOR(LN(ABS(diff))/LN(10))1) > AS magnitude, > diff,batchTot > FROM > (SELECT batchTot13356 AS diff, batchTot > FROM > (SELECT SUM(v) AS batchTot FROM incorrect) > t1) t2) t3) t4) t5 > ; +++  v  investigate  +++  2460.00  *******   1452.00    1450.00    1610.00    1772.00    1160.00    1574.00  *******   1698.00   +++
You need to make some minor changes to get this to work on other platforms: