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Sunday Times Teaser 3183 – Partial Eclipse

by BRG on September 22, 2023

by John Owen

Alf, Bert and Charlie were comparing their experiences of the eclipse from different locations. The moon appeared to be exactly the same size as the sun as it passed in front of part of the sun’s disc. The magnitude of an eclipse measures the maximum part of the diameter of the sun’s disc that is obscured. Taking the apparent diameter of the sun as 100, they noted the following:

Alf: “My magnitude was a whole number”. Bert: “If I took the part of the sun’s circumference that was obscured, multiplied it by the radius and then subtracted the area of the sun’s disc that was obscured, I also got a whole number”.

Charlie: “Both of those statements are true for all of us, but we all saw different magnitudes greater than 10”.

In increasing order, what were those three magnitudes?

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3 Comments Leave one →
  1. BRG permalink

    • Frits permalink


      You can also deduce that the magnitude must be even otherwise the result of Bert’s calculation is not a whole number (both s and (d – m) would be odd).

      • BRG permalink

        Yes, I noticed that too but I was too lazy to add the comment so I took the easy way
        out. I will add the comment in an update though since the m loop can be shorter.

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