27

Part of 2019 India PRMO

Problems(2)

Combinatorics Question

Source:

We will say that a rearrangement of the letters of a word has no fixed letters if, when the rearrangement is placed directly below the word, no column has the same letter repeated. For instance

HBRATA

is a rearragnement with no fixed letter of

BHARAT

. How many distinguishable rearrangements with no fixed letters does

BHARAT

A

s are considered identical.)

combinatoricscountingdistinguishability

Honey and The Ant

Source: PRMO Leg 2 P27

A conical glass is in the form of a right circular cone. The slant height is

21

and the radius of the top rim of the glass is

14

. An ant at the mid point of a slant line on the outside wall of the glass sees a honey drop diametrically opposite to it on the inside wall of the glass. If

d

the shortest distance it should crawl to reach the honey drop, what is the integer part of

d

?
https://i.imgur.com/T1Y3zwR.png

geometryPRMOcone