MathDB

21

Part of 2022 MIG

Problems(2)

2022 A Individual #21

Source:

4/28/2022
Let T(p)T(p) denote the number of right triangles with integer side lengths and one of its side lengths being pp. Which of the following values of pp produces the greatest possible value of T(p)T(p) among all five answer choices?
<spanclass=′latex−bold′>(A)</span>24<spanclass=′latex−bold′>(B)</span>27<spanclass=′latex−bold′>(C)</span>28<spanclass=′latex−bold′>(D)</span>36<spanclass=′latex−bold′>(E)</span>54<span class='latex-bold'>(A) </span>24\qquad<span class='latex-bold'>(B) </span>27\qquad<span class='latex-bold'>(C) </span>28\qquad<span class='latex-bold'>(D) </span>36\qquad<span class='latex-bold'>(E) </span>54
2022 A Individual
2022 B Individual #21

Source:

4/30/2022
A herder has forgotten the number of cows she has, and does not want to count them all of them. She remembers these four facts about the number of cows:
[*]It has 33 digits. [*]It is a palindrome. [*]The middle digit is a multiple of 44. [*]It is divisible by 1111.
What is the sum of all possible numbers of cows that the herder has?
<spanclass=′latex−bold′>(A)</span>343<spanclass=′latex−bold′>(B)</span>494<spanclass=′latex−bold′>(C)</span>615<spanclass=′latex−bold′>(D)</span>635<spanclass=′latex−bold′>(E)</span>726<span class='latex-bold'>(A) </span>343\qquad<span class='latex-bold'>(B) </span>494\qquad<span class='latex-bold'>(C) </span>615\qquad<span class='latex-bold'>(D) </span>635\qquad<span class='latex-bold'>(E) </span>726
2022 B Individual