One way to estimate progress in weightlifting, and figure out a workout regimen that will continue to build strength, is by using one's one-rep max as a measurement. A one-rep max is the maximum amount of weight that can be lifted in one repitition of whatever lift is being measured, be it bench press, squat, dead lift or etc. However, directly measuring a max by lifting it on a bar is dangerous without a spotter (even more dangerous than normal lifting without a spotter, that is), as overestimating the weight can leave one trapped under the bar. Also, if the weight is increased until max is found, say, from 100 to 110 to 120, fatigue may cause the amount which is eventually stumbled upon to be slightly lower than one's actual max.

Solving this problem is a matter of doing multiple lifts with slightly lower than maximum weight on the bar. Using a table like the one below, one can estimate how much their actual one-rep max would be, to generally within a few percentage points of the actual figure. The table gives a list of coefficients, which are multiplied by the actual weight lifted for the specified number of reps. That is, if one can lift 105 lbs. of weight 7 times, their max is around 105 lbs * 1.226 = 128.73 lbs. Because this is just an estimate, a safe figure to give as the max in this case would be 125 lbs. Also, note that the estimates become less accurate as the reps get higher -- even though numbers are given, I personally wouldn't trust any figure taken by doing more than 10 reps.

``` Reps         Coefficient
1                1       (most accurate)
2              1.050
3              1.088
4              1.125
5              1.160
6              1.190
7              1.225
8              1.256
9              1.290
10             1.325
11             1.355
12             1.388
13             1.432
14             1.457
15             1.495     (least accurate)
```

How these numbers were generated: Because I don't have any special insight into the abilities of the human body, I was forced to use other people's numbers. To avoid copyright issues, I found two tables online, each with slightly different numbers; these were averaged together. Then, I randomly generated a table of modifiers which would add or subtract .001 or .002 (but never 0) from each coefficient -- this way, even if one of the original tables is known the other cannot be derived from the figures I give above. Accuracy suffers slightly from this, but the values in both tables all have less than 2% difference from the values given in mine.