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- Since these lists tend to overlap quite a bit, invitations are usually given to students "further down" these lists until22 KB (3,532 words) - 10:25, 27 September 2024
- ...ximum value (typically to <math>2^{31}-1</math> for signed <math>32</math>-bit integers). Integers in Python can be of arbitrary size, theoretically limit2 KB (296 words) - 14:04, 5 August 2022
- Using a little bit of ingenuity, we note that Let's simplify a bit further, where we use our recursion for <math>S_{n-2}</math>.10 KB (1,702 words) - 21:23, 25 July 2024
- ...math>, thus eliminating answer choice (A). <math>r</math> is only a little bit bigger than half of <math>s</math>, so we can reasonably assume that their6 KB (958 words) - 22:29, 28 September 2023
- Trying out the values for a bit leads to us getting <math>34</math> with <math>(-3, -2, 2, 6)</math> in 1 s3 KB (584 words) - 00:17, 17 July 2024
- ...ously <math>6^{83}+8^{83}</math> we look for a pattern with others. With a bit of digging, we discover that <math>6^n+6^m</math> where <math>m</math> and3 KB (361 words) - 19:20, 14 January 2023
- A little bit of checking tells us that the units digit must be 2. Now our cube must be i ==Solution 6 (A bit of brute force using basic knowledge.)==6 KB (893 words) - 07:15, 2 February 2023
- We can cheat a little bit and approximate, since we are dealing with such large numbers. As above, <m6 KB (874 words) - 14:50, 20 January 2024
- ...equations, we get <math>x = 0</math>. Solving for <math>y,z</math> with a bit of effort, we eventually get <math>x = 0</math>, <math>y = \frac {291}{2\sq7 KB (1,086 words) - 07:16, 29 July 2023
- == Solution 3 (A bit more math involved) ==6 KB (926 words) - 12:18, 12 October 2024
- ...length 8 of the rectangle (any other inscribed rectangle can be rotated a bit, then made smaller; this one can't because then the rectangle cannot be ins3 KB (601 words) - 08:25, 19 November 2023
- === Solution 3 === <!-- I would put this solution first, but needs a bit of formatting for clarity - azjps -->5 KB (710 words) - 20:04, 14 September 2020
- ...>, so <math>1000/y=9-1/x</math>. <math>1000/y</math> must be just a little bit smaller than 9, so we find <math>y=112</math>, <math>x=14</math>, and the s2 KB (375 words) - 18:34, 4 August 2021
- ...</math>, <math>x = 0</math>, and <math>y = 20</math>. After doing a little bit of algebra, the intersections are the lines <cmath>y = -2x + 10</cmath> <cm7 KB (1,084 words) - 10:48, 13 August 2023
- A bit of trial and error and observing patterns leads to the answer <math>480</ma6 KB (913 words) - 15:34, 6 August 2020
- Here's a bit of intuition behind the solution. If I wanted to travel to some point on th6 KB (1,042 words) - 14:08, 1 January 2025
- ...distinct, we try to find a function which fulfills the given conditions. A bit of trial and error would lead to the [[cosine]] function: <math>f(x) = \cos5 KB (921 words) - 15:36, 28 November 2024
- Adding, we get <math>2480</math>, with a bit extra, so our answer is <math>\boxed{248}</math>.6 KB (867 words) - 11:49, 17 November 2024
- If we work with the problem for a little bit, we quickly see that there is no direct combinatorics way to calculate <mat7 KB (1,011 words) - 19:09, 4 January 2024
- The wording of this problem is a bit dissatisfying and could have been improved by stating that there are at lea6 KB (958 words) - 15:41, 30 November 2024