Table of Transposed Numbers.
Reading edition
DIFFERENCES.
9{ 10213243 54657687 98
011223 34455667 7889
18{ 20314253 64758697
021324 35465768 79
27{ 30415263 748596
031425 36475869
36{ 40516273 8495
041526 374859
45{ 50617283 94
051627 3849
54{ 60718293
061728 39
63{ 708192
071829
72{ 8091
0819
81{ 90
09
90{ 100
010
99{ 100
001
Explanation of Foregoing Table.
The transposition of figures is a frequent cause of errors in proving accounts and balance sheets. This table is founded on the fact that all differences between transposed numbers are multiples of nine. The difference between the figures misplaced is equal to the quotient of the resulting error when divided by nine; thus, 91 - 19 = 72; 72 ÷ 9 = 8; 9 - 1 = 8, and the labor of searching for it may be confined to examining those figures the transposition of which would make the difference, as they are the only ones that can cause the error. Thus: if the error in the balance-sheet be 81 cents, it is possibly caused by a transposition, and the clerk can first examine the cents column of his books for items of 90 cents, or 09 cents, alone, with a strong probability of finding the cause of the error without further revision. Transpositions may occur in any decimal or integer place, and the differences caused thereby are divisible by nine without a remainder; but, beyond this table, the numbers ascend in regular progression, each difference increasing by nine, as follows:
108 {120 ;117 {130 ;126 {140 ;etc.
121314
The quotient of the difference in a regular progression, when divided by nine, gives the figures transposed, thus: 130 - 13 = 117 ÷ 9 = 13, which are the figures to be sought for when a discrepancy of 117 is shown; but this will not apply to differences below 81, nor to mixed transpositions. An error divisible by two may be caused by posting an item to the wrong side of the ledger.