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Using the digits 1 to 9, create three 3-digit numbers. The second number is twice the first. The third number is three times the first.

[Ref: ZGEB] Submitted by Adailton J. Chiaradia.

Hint: The first number starts with 3.

Answer:

Puzzle 417

What is represented by this BrainBat?

Dr Dr

[Ref: ZJBU]

Hint: Say what you see.

Answer: A paradox: a pair of Docs.

Or Paramedics: a pair of medics.

Puzzle 418

Below, 10 nine letter words have been broken into chunks of three letters. These chunks have been mixed up, no chunk is used twice and all chunks are used. Can you determine what the 10 words are?

som one dbr pen rtm ber
nes ent ive eph eti ens
mes off eak eid sep win
erd tel day ter wed tem
aft apa own car ern oon

Which square, which circle, and which triangle has the closest area to the doughnut shape on the left? The drawings are to scale, so you might be able to judge it, as well as working the actual areas out.

The larger circle has diameter = 4, therefore the radius is 2, and the area is π x 2^{2} = 4π.

The smaller circle has diameter = 2, therefore the radius is 1, and the area is π x 1^{2} = π.

Therefore the shaded area is 4π - π = 3π ≈ 9.42.

Circle

The area of a circle is π x Radius^{2}.

The circle with diameter 3.1 has a radius of 1.55 and an area of π x 1.55^{2} = 7.55.

The circle with diameter 3.5 has a radius of 1.75 and an area of π x 1.75^{2} = 9.62 (** closest match).

The circle with diameter 3.9 has a radius of 1.95 and an area of π x 1.95^{2} = 11.95.

Square

The area of a square is Side x Side.

The square with side 3.1 has an area of 3.1 x 3.1 = 9.61 (** closest match).

The square with side 3.5 has an area of 3.5 x 3.5 = 12.25.

The square with side 3.9 has an area of 3.9 x 3.9 = 15.21.

Triangle

The area of a triangle is ½ x Base x Height. Using Pythagoras' theorem it can be shown that the area of an equilateral triangle is Sqrt(3) x Base^{2} ÷ 4.

The triangle with side 3.9 has an area of Sqrt(3) x 3.9 x 3.9 ÷ 4 = 6.59.

The triangle with side 4.3 has an area of Sqrt(3) x 4.3 x 4.3 ÷ 4 = 8.01.

The triangle with side 4.7 has an area of Sqrt(3) x 4.7 x 4.7 ÷ 4 = 9.57 (** closest match).

Puzzle 420

Using the BrainTracker grid below, how many words can you find? Each word must contain the central K and no letter can be used twice, however, the letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?

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