Egg Cartons - Maths Olympiad Problems | Maths Contest Problems | PRMO Questions | NSEJS Maths Questions | NTSE Stage 2

 Egg Cartons

Maths Olympiad Problems | Maths Contest Problems | PRMO Questions | NSEJS Maths Questions Important for ---- NTSE Stage 2, Maths Olympiads, PRMO, RMO, INMOZoe decided to investigate the number of different ways of placing identical eggs in clear rectangular cartons of various sizes.

For example, there is only one way of placing six eggs in a 2 × 3 carton and only two different ways of placing five eggs.

Reflections and rotations of arrangements are not considered different. For example, all of these arrangements are the same

a)  Here are two ways of arranging four eggs in a 2 × 3 carton.

            Draw four more different ways. 

b)  Draw six different ways of arranging two eggs in a 2 × 3 carton.

 

c)  Draw six different ways of arranging three eggs in a 2 × 3 carton. 

d)  Draw all the different ways of arranging six eggs in a 2 × 4 carton.

Solutions:

a)  

For each of these arrangements, any rotation or reflection is acceptable.

b) 

For each of these arrangements, any rotation or reflection is acceptable.

c) 

For each of these arrangements, any rotation or reflection is acceptable.

d) Each arrangement of six eggs in a 2 × 4 carton has two empty positions. By systematically locating the two empty positions, we see that there are ten different ways to arrange six eggs in a 2 × 4 carton

For each of these arrangements, any rotation or reflection is acceptable.