
ZOJ Problem Set  3793
Benford's Law, also called the FirstDigit Law, refers to the frequency distribution of digits in many (but not all) reallife sources of data. In this distribution, the number 1 occurs as the leading digit about 30% of the time, while larger numbers occur in that position less frequently: 9 as the first digit less than 5% of the time. Benford's Law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution. This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude. A set of numbers is said to satisfy Benford's Law if the leading digit d ∈ {1, ..., 9} occurs with probability P(d) = log_{10}(d + 1)  log_{10}(d). Numerically, the leading digits have the following distribution in Benford's Law:
Now your task is to predict the first digit of b^{e}, while b and e are two random integer generated by discrete uniform distribution in [1, 1000]. Your accuracy rate should be greater than or equal to 25% but less than 60%. This is not a school exam, and high accuracy rate makes you fail in this task. Good luck! InputThere are multiple test cases. The first line of input contains an integer T (about 10000) indicating the number of test cases. For each test case: There are two integers b and e (1 <= b, e <= 1000). OutputFor each test case, output the predicted first digit. Your accuracy rate should be greater than or equal to 25% but less than 60%. Sample Input20 206 774 133 931 420 238 398 872 277 137 717 399 820 754 997 463 77 791 295 345 375 501 102 666 95 172 462 893 509 839 20 315 418 71 644 498 508 459 358 767 Sample Output8 2 2 1 4 2 1 2 1 1 4 6 2 4 9 7 2 7 1 7 HintThe actual first digits of the sample are 8, 2, 2, 1, 4, 2, 1, 2, 1, 1, 3, 5, 1, 3, 8, 6, 1, 6, 9 and 6 respectively. The sample output gets the first 10 cases right, so it has an accuracy rate of 50%. ReferenceAuthor: ZHOU, Yuchen Source: ZOJ Monthly, June 2014 