MathDB

Problem 4

Part of 2019 LIMIT Category A

Problems(2)

counting 5x5 grids

Source: LIMIT 2019 CAS1 P4

4/28/2021
How many 5×55\times5 grids are possible such that each element is either 00 or 11 and each row sum and column sum is 44? <spanclass=′latex−bold′>(A)</span> 64<span class='latex-bold'>(A)</span>~64 <spanclass=′latex−bold′>(B)</span> 32<span class='latex-bold'>(B)</span>~32 <spanclass=′latex−bold′>(C)</span> 120<span class='latex-bold'>(C)</span>~120 <spanclass=′latex−bold′>(D)</span> 96<span class='latex-bold'>(D)</span>~96
combinatorics
tangents to circle from point

Source: LIMIT 2019 CAS2 P4

4/28/2021
From a point PP outside of a circle with centre OO, tangent segments PA‾\overline{PA} and PB‾\overline{PB} are drawn. If 1∣OA‾∣2+1∣PA‾∣2=116\frac1{\left|\overline{OA}\right|^2}+\frac1{\left|\overline{PA}\right|^2}=\frac1{16}, then ∣AB‾∣=\left|\overline{AB}\right|=? <spanclass=′latex−bold′>(A)</span> 4<span class='latex-bold'>(A)</span>~4 <spanclass=′latex−bold′>(B)</span> 6<span class='latex-bold'>(B)</span>~6 <spanclass=′latex−bold′>(C)</span> 8<span class='latex-bold'>(C)</span>~8 <spanclass=′latex−bold′>(D)</span> 10<span class='latex-bold'>(D)</span>~10
geometry