| align="right" | 2 || 0.00274 || align="right" | 3 | 0.00820 |----- | 0.05 || 0.32029 = 6.11916 | align="right" | 6 || 0.04046 || align="right" | 7 || 0.05624 |----- | 0.1 | 0.45904 = 8.77002 | align="right" | 8 || 0.07434 || align="right" | 9 | 0.09462 |----- | 0.2 | 0.66805 = 12.76302 | align="right" | 12 || 0.16702 || align="right" | 13 | 0.19441 |----- | 0.3 || 0.84460 = 16.13607 | align="right" | 16 || 0.28360 || align="right" | 17 || 0.31501 |----- | 0.5 || 1.17741 = 22.49439 | align="right" | 22 || 0.47570 || align="right" | 23 || 0.50730 |----- | 0.7 || 1.55176 = 29.64625 | align="right" | 29 || 0.68097 || align="right" | 30 || 0.70632 |----- | 0.8 || 1.79412 = 34.27666 | align="right" | 34 || 0.79532 || align="right" | 35 || 0.81438 |----- | 0.9 || 2.14597 = 40.99862 | align="right" | 40 || 0.89123 || align="right" | 41 || 0.90315 |----- | 0.95 || 2.44775 = 46.76414 | align="right" | 46 || 0.94825 || align="right" | 47 || 0.95477 |----- | 0.99 | 3.03485 = 57.98081 | align="right" | 57 | 0.99012 | align="right" | 58 || 0.99166 |} Some values falling outside the bounds have been colored to show that the approximation is not always exact. Partition problem A related problem is the partition problem, a variant of the knapsack problem from operations research. Some weights are put on a balance scale; each weight is an integer number of grams randomly chosen between one gram and one million grams (one tonne). The question is whether one can usually (that is, with probability close to 1) transfer the weights between the left and right arms to balance the scale. (In case the sum of all the weights is an odd number of grams, a discrepancy of one gram is allowed.) If there are only two or three weights, the answer is very clearly no; although there are some combinations which work, the majority of randomly selected combinations of three weights do not. If there are very many weights, the answer is clearly yes. The question is, how many are just sufficient? That is, what is the number of weights such that it is equally likely for it to be possible to balance them as it is to be impossible? Often, people's intuition is that the answer