We show that the least number of cells (the gap number) one needs to take out from a rectangle with integer sides of length at least 2 in order to be tiled by ribbon right trominoes is less than or equal to 4. If the sides of the rectangle are of length at least 5, then the gap number is less than or equal to 3. We also show that for the family of rectangles that have nontrivial minimal number of gaps, with probability 1, the only obstructions to tiling appear from coloring invariants. This is in contrast to what happens for simply connected regions. For that class of regions Conway and Lagarias found a tiling invariant that does not follow from coloring.
Although accreditation standards require that programs must teach quantitative research methodology, students are not always eager to learn statistics. This article describes several techniques to aid the social work instructor in engaging students who are uncomfortable facing statistical information. In one small BSW program a social work professor has collaborated with a mathematics professor in developing ideas to engage students who arrive with fear and loathing at the very word statistics. By promoting problem solving, improving student attitudes, and quelling fears regarding learning statistics, these techniques can be adapted in the social work classroom.
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