MathDB

Centuries ago, the pirate Captain Blackboard buried a vast amount of treasure in a single cell of a

2 \times 4

grid-structured island. Treasure was buried in a single cell of an

M\times N

(

2\le M

N

) grid. You and your crew have reached the island and have brought special treasure detectors to find the cell with the treasure For each detector, you can set it up to scan a specific subgrid

[a,b]\times[c,d]

with

1\le a\le b\le 2

and

1\le c\le d\le 4

. Running the detector will tell you whether the treasure is in the region or not, though it cannot say where in the region the treasure was detected. You plan on setting up

Q

detectors, which may only be run simultaneously after all

Q

detectors are ready. What is the minimum

Q

required to gaurantee to determine the location of the Blackboard’s legendary treasure?

Problem Statement