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2017 InIMC keystage2-EMIC team Question 6

xIMC · 2017 InIMC keystage2-EMIC team

Question 6

In the diagram, eight of the numbers from 1 to 10 are used to fill the squares $A,B,C,D,\mathrm{I},\mathrm{II},\mathrm{III},\mathrm{IV}$. The numbers in $\mathrm{I},\mathrm{II},\mathrm{III},\mathrm{IV}$ are the sums of their two neighbors. List down all the possible solutions. (Rotations and reflections are allowed).

Question illustration

Question illustration