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MathNet 2026 — Part 02 Question 99

Math Olympiad Vault · MathNet 2026 — Part 02

Question 99

Amanda drew the following figure: Question illustration Note that the sum along any side of the triangle above is always the same, since, as we can see, $$
1+3+6=6+2+2=1+7+2
$$
a) Complete the missing numbers Circles in the figure below so that the sums along any side of the square are always the same. Question illustration
b) Find a way to place the numbers in the circles so that the sums along any line are always the same. Is there more than one solution? Question illustration
c) $\mathrm{Na}$ Figure below, which was designed only partially (due to lack of space!), it is also worthwhile that the sum along each segment is always the same. However, Amanda deleted all numbers except the two numbers shown in figure (3 and 4). It is known that there are 40 circles in the drawing. Is it possible to find out what numbers were in the circles painted light gray and dark gray? Question illustration