AMC 10 Exercise – 2

Posted on October 20, 2024 by kevin
  1. What is the tens digit of $2019^{2020}-2021$?
  2. All the numbers $2$,$3$,$4$,$5$ are assigned to the four faces of a tetrahedron. For each of the four vertices of the tetrahedron, a product of three numbers are computed, where the three numbers are the numbers assigned to the three faces that include that vertex. Then the sum of these four products is calculated. What is the difference between the greatest and the smallest possible values of the sum?
  3. All the numbers $2$,$3$,$4$,$5$,$6$,$7$ are assigned to the six faces of a cube, one number to each face. For each of the eight vertices of the cube, a product of three numbers is computed, where the three numbers are the numbers assigned to the three faces that include that vertex. What is the greatest possible value of the sum of these eight products?
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