MathDB

80

Part of 1985 IMO Longlists

Problems(1)

Collection of 4x4 matrices

Source:

9/14/2010
Let E={1,2,…,16}E = \{1, 2, \dots , 16\} and let MM be the collection of all 4×44 \times 4 matrices whose entries are distinct members of EE. If a matrix A=(aij)4×4A = (a_{ij} )_{4\times4} is chosen randomly from MM, compute the probability p(k)p(k) of max⁡imin⁡jaij=k\max_i \min_j a_{ij} = k for k∈Ek \in E. Furthermore, determine l∈El \in E such that p(l)=max⁡{p(k)∣k∈E}.p(l) = \max \{p(k) | k \in E \}.
linear algebramatrixprobability