MathDB

14

Part of 2019 AMC 10

Problems(2)

Lines in a plane

Source: 2019 AMC 10A #14 / AMC 12A #8

2/8/2019
For a set of four distinct lines in a plane, there are exactly NN distinct points that lie on two or more of the lines. What is the sum of all possible values of NN?
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>16<spanclass=′latex−bold′>(C)</span>18<spanclass=′latex−bold′>(D)</span>19<spanclass=′latex−bold′>(E)</span>21<span class='latex-bold'>(A) </span> 14 \qquad <span class='latex-bold'>(B) </span> 16 \qquad <span class='latex-bold'>(C) </span> 18 \qquad <span class='latex-bold'>(D) </span> 19 \qquad <span class='latex-bold'>(E) </span> 21
AMCAMC 102019 AMC 12A2019 AMC 10A2019 AMCAMC 12counting
Factorial Madness

Source: 2019 AMC 10B #14

2/14/2019
The base-ten representation for 19!19! is 121,6T5,100,40M,832,H00121,6T5,100,40M,832,H00, where TT, MM, and HH denote digits that are not given. What is T+M+HT+M+H?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>8<spanclass=′latex−bold′>(C)</span>12<spanclass=′latex−bold′>(D)</span>14<spanclass=′latex−bold′>(E)</span>17<span class='latex-bold'>(A) </span>3 \qquad<span class='latex-bold'>(B) </span>8 \qquad<span class='latex-bold'>(C) </span>12 \qquad<span class='latex-bold'>(D) </span>14 \qquad<span class='latex-bold'>(E) </span> 17
factorial2019 AMC2019 AMC 10BAMC 10AMC