Skip to content / Đến nội dung
ThichHocToan.com

MathNet 2003 — Part 02 Question 19

Math Olympiad Vault · MathNet 2003 — Part 02

Question 19

A square sided numeric keypad $4$ has $16$ keys numbered $1$ to $16$. Agent $007$ must press two buttons at the same time to enter the enemy base, and if he gets it wrong he will sound the alarm. However, it only knows that the two keys are not contiguous (i.e. they do not have a common edge or vertex). What is the probability that he will be able to infiltrate?
  1. $\frac{1}{64}$
  2. $\frac{1}{78}$
  3. $\frac{1}{128}$
  4. $\frac{1}{156}$
  5. $\frac{1}{160}$.