MathDB

16

Part of 2021 MOAA

Problems(2)

Team Round P16

Source:

10/16/2021
Let △ABC\triangle ABC have ∠ABC=67∘\angle ABC=67^{\circ}. Point XX is chosen such that AB=XCAB = XC, ∠XAC=32∘\angle{XAC}=32^\circ, and ∠XCA=35∘\angle{XCA}=35^\circ. Compute ∠BAC\angle{BAC} in degrees.
Proposed by Raina Yang
MOAA 2021team
Gunga P16

Source:

10/16/2021
Let 1,7,19,…1,7,19,\ldots be the sequence of numbers such that for all integers n≥1n\ge 1, the average of the first nn terms is equal to the nnth perfect square. Compute the last three digits of the 20212021st term in the sequence.
Proposed by Nathan Xiong
MOAA 2021Gunga