2.7 1.3

Part of 2021 CMIMC

Problems(2)

2021 Geo Div 1 P3 (Div 2 P7)

Source:

\triangle ABC

be a triangle with

AB=10

AC=16,

I

be the intersection of the internal angle bisectors of

\triangle ABC.

Suppose the tangents to the circumcircle of

\triangle BIC

B

C

intersect at a point

P

PA=8.

Compute the length of

{BC}.

Proposed by Kyle Lee

2021 Combo Div 1 P3 (Div 2 P7)

Source:

How many permutations of the string

0123456

are there such that no contiguous substrings of lengths

1<\ell<7

have a sum of digits divisible by

7

?
Proposed by Srinivasan Sathiamurthy