Quiz: Can You Solve This Sum ?

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[Hint]: Think out of the box…

Answer below (scroll down)
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Answer:
1 + 13 + 15 = 30 in 9 Based Numeric System.
i. e. 1 + 12 + 14 = 27 in Base10

Explain: In Base 9
{1}_{9} = 1.9  = {1}_{10}
{13}_{9} = 1.9 + 3 = {12}_{10}
{15}_{9} = 1.9 + 5 = {14}_{10}
{30}_{9} = 3.9 + 0 = {27}_{10}

Quiz

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In the diagram, the circumference of the external large circle is
1) longer, or
2) shorter, or
3) equal to,
the sum of the circumferences of all inner circles centered on the common diameter, tangent to each other.

Answer: 3) equal

circumference = π. diameter

Let d be the diameter of the external large circle C
Let dj be the diameter of the inner circle Cj

\displaystyle d = \sum_{j} d_j
\displaystyle \pi. d = \pi. \sum_{j} d_j= \sum_{j}\pi.d_j

Circumference of the external circle
= sum of circumferences of all inner circles