Rectangles in a Cross
Difficulty: Medium · Topics: Discrete Mathematics, Combinatorics, Counting
Xochsimon shakldagi to‘g‘ri to‘rtburchaklar
The figure below is built from 24 unit squares.
graph "x":[-0.45,6.45],"y":[-0.45,5.45],"axes":false,"ink":true,"label":"A figure built from 24 unit squares","items":["type":"line","from":[0,0],"to":[0,5],"ink":true,"type":"line","from":[1,0],"to":[1,5],"ink":true,"type":"line","from":[2,0],"to":[2,5],"ink":true,"type":"line","from":[3,0],"to":[3,5],"ink":true,"type":"line","from":[4,1],"to":[4,4],"ink":true,"type":"line","from":[5,1],"to":[5,4],"ink":true,"type":"line","from":[6,1],"to":[6,4],"ink":true,"type":"line","from":[0,0],"to":[3,0],"ink":true,"type":"line","from":[0,1],"to":[6,1],"ink":true,"type":"line","from":[0,2],"to":[6,2],"ink":true,"type":"line","from":[0,3],"to":[6,3],"ink":true,"type":"line","from":[0,4],"to":[6,4],"ink":true,"type":"line","from":[0,5],"to":[3,5],"ink":true]
According to this, how many different rectangles are there in the figure?
Quyidagi shakl 24 ta birlik kvadratdan tuzilgan.
graph "x":[-0.45,6.45],"y":[-0.45,5.45],"axes":false,"ink":true,"label":"A figure built from 24 unit squares","items":["type":"line","from":[0,0],"to":[0,5],"ink":true,"type":"line","from":[1,0],"to":[1,5],"ink":true,"type":"line","from":[2,0],"to":[2,5],"ink":true,"type":"line","from":[3,0],"to":[3,5],"ink":true,"type":"line","from":[4,1],"to":[4,4],"ink":true,"type":"line","from":[5,1],"to":[5,4],"ink":true,"type":"line","from":[6,1],"to":[6,4],"ink":true,"type":"line","from":[0,0],"to":[3,0],"ink":true,"type":"line","from":[0,1],"to":[6,1],"ink":true,"type":"line","from":[0,2],"to":[6,2],"ink":true,"type":"line","from":[0,3],"to":[6,3],"ink":true,"type":"line","from":[0,4],"to":[6,4],"ink":true,"type":"line","from":[0,5],"to":[3,5],"ink":true]
Shunga ko‘ra, shaklda nechta turli to‘g‘ri to‘rtburchak bor?