VTMO 2021 — Grade 4 — vtmo Question 10

Question 10

Labels $A , B , C , D , E$ are Apple, Grape, Orange, Cherry, Plum, all wrong. Swapping only $A \text{--} B , B \text{--} C$, or $C \text{--} D$ leaves exactly $4$ wrong labels in each case. Which actual $A \text{--} E$ fruit order is possible?

Question illustration

Grape–Orange–Plum–Apple–Cherry
Plum–Apple–Grape–Orange–Cherry
Grape–Orange–Apple–Plum–Cherry
Plum–Apple–Cherry–Grape–Orange
Orange–Apple–Grape–Plum–Cherry