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Question 16

The diagram shows the net of a cube, that is, we can fold along the edges of the squares to
make a cube from this net. On each face there is an integer writtenΒ - $$1,a,b,c,d,2026$$. Each of the four numbers $$a,b,c,d$$ equals the average of the numbers on the four faces ofΒ the cube adjacent to it, The value of $$a$$ is

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Correct Answer: 811

From the net, the opposite face pairs are $$a$$ with $$2026$$, $$b$$ with $$c$$, and $$d$$ with $$1$$. Thus the averaging conditions give $$4a=b+c+d+1$$, $$4b=a+d+2027$$, $$4c=a+d+2027$$ and $$4d=a+b+c+2026$$. Solving this system gives $$a=811$$, so the requested value is $$811$$.

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