12

Part of 2017 QEDMO 15th

Problems(2)

2 octahedra with sides 1-16 such each side has same probability with sum

Source: 15th -a QEDMO problem 12 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

Jorn wants to cheat at the role play: he intends to cheat the sides to re-label its two octahedra, so that each of the numbers from

1

16

has the same probability as the sum of the dice occurs. So that the game master does not notice this so easily, he only wants to use numbers from

0

8

, if necessary several times or not at all. Is this possible?

probabilitycombinatorics

for which n is a^n + 1/a^n integer if (a +1/a )^2=11 ?

Source: 15th -b QEDMO problem 12 (19. - 22. 10. 2017) https://artofproblemsolving.com/community/c1512515_qedmo_2005

a

be a real number such that

\left(a + \frac{1}{a}\right)^2=11

n\in N

a^n + \frac{1}{a^n}

an integer? Does this depend on the exact value of

a