MathDB

Harry Potter can do any of the three tricks arbitrary number of times:

i)

switch

1

plum and

1

pear with

2

apples

ii)

switch

1

pear and

1

apple with

3

plums

iii)

switch

1

apple and

1

plum with

4

pears In the beginning, Harry had

2012

of plums, apples and pears, each. Harry did some tricks and now he has

2012

apples,

2012

pears and more than

2012

plums. What is the minimal number of plums he can have?

Problem Statement