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Whenever you transpose two digits in a number the error is ALWAYS divisible by 9. In fact the error is always either
09, 18, 27, 36, 45, 54, 63, 72, 81 or 90. If you add up the two digits of all of these numbers you will see that (in
addition to the number being a multiple of nine) the digits also add up to 9.
In fact the errors can be any of these numbers multiplied by any fact of 10 as well (eg 09,90,900,9000 or 18, 180, 1800 etc)
If you look up the error amount in this table it will tell you what are the possible combinations of numbers which
can be transposed to make up that error - eg if the error is 36 then the numbers could be 15 and 51 or 48 and 84 etc)
| Difference=09 |
|---|
| Amt1 | Amt2 |
| 01 | 10 |
| 10 | 01 |
| 12 | 21 |
| 21 | 12 |
| 23 | 32 |
| 32 | 23 |
| 34 | 43 |
| 43 | 34 |
| 45 | 54 |
| 54 | 45 |
| 56 | 65 |
| 65 | 56 |
| 67 | 76 |
| 76 | 67 |
| 78 | 87 |
| 87 | 78 |
| 89 | 98 |
| 98 | 89 |
|
| Difference=18 |
|---|
| Amt1 | Amt2 |
| 02 | 20 |
| 13 | 31 |
| 20 | 02 |
| 24 | 42 |
| 31 | 13 |
| 35 | 53 |
| 42 | 24 |
| 46 | 64 |
| 53 | 35 |
| 57 | 75 |
| 64 | 46 |
| 68 | 86 |
| 75 | 57 |
| 79 | 97 |
| 86 | 86 |
| 97 | 79 |
|
| Difference=27 |
|---|
| Amt1 | Amt2 |
| 03 | 30 |
| 14 | 41 |
| 25 | 52 |
| 30 | 03 |
| 36 | 63 |
| 41 | 14 |
| 47 | 74 |
| 52 | 25 |
| 58 | 85 |
| 63 | 36 |
| 69 | 96 |
| 74 | 47 |
| 85 | 58 |
| 96 | 69 |
|
| Difference=36 |
|---|
| Amt1 | Amt2 |
| 04 | 40 |
| 15 | 51 |
| 26 | 62 |
| 37 | 73 |
| 40 | 04 |
| 48 | 84 |
| 51 | 15 |
| 59 | 95 |
| 62 | 26 |
| 73 | 37 |
| 84 | 48 |
| 95 | 59 |
|
| Difference=45 |
|---|
| Amt1 | Amt2 |
| 05 | 50 |
| 16 | 61 |
| 27 | 72 |
| 38 | 83 |
| 49 | 94 |
| 50 | 05 |
| 61 | 16 |
| 72 | 27 |
| 83 | 38 |
| 94 | 49 |
|
| Difference=54 |
|---|
| Amt1 | Amt2 |
| 06 | 60 |
| 17 | 71 |
| 28 | 82 |
| 39 | 93 |
| 60 | 06 |
| 71 | 17 |
| 82 | 28 |
| 93 | 39 |
|
| Difference=63 |
|---|
| Amt1 | Amt2 |
| 07 | 70 |
| 18 | 81 |
| 29 | 92 |
| 70 | 07 |
| 81 | 18 |
| 92 | 29 |
|
| Difference=72 |
|---|
| Amt1 | Amt2 |
| 08 | 80 |
| 19 | 91 |
| 80 | 08 |
| 91 | 19 |
|
| Difference=81 |
|---|
| Amt1 | Amt2 |
| 09 | 90 |
| 90 | 09 |
|
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