# [Enigma] Small problems

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• Aug 13th 2008, 05:59 AM
z1llch
Quote:

Originally Posted by Moo
What about 1 as a factor ?

Since the girl can't know what the numbers are, *major hint* you have to find the triplets whose product is equal and whose sum is equal (Tongueout)

i still don't get this..
• Aug 13th 2008, 08:34 AM
Soroban
Hello, Moo!

Quote:

3) Simple geometry
The Swedish flag has a yellow cross of constant width in a blue background.
The yellow area represents one-third of the flag's area.
If the flag is 1m long and 66cm wide, what is the width of the yellow stripes ?

The stripes comprising the cross can be "moved" to the edges of the flag.
Let $\displaystyle x$ = width of the stripe (cm).
Code:

              100       * - - - - - - - - *       |                | x       |  * - - - - - - *   66 |  |            |       |  |            | 66-x       |  |            |       * - * - - - - - - *         x      100-x

The blue region's area is: .$\displaystyle \frac{2}{3} \times (66\cdot100) \:=\;4400$ cm²

It is also: .$\displaystyle (100-x)(66-x)$ cm²

Hence, we have: .$\displaystyle (100-x)(66-x) \:=\:4400 \quad\Rightarrow\quad x^2 - 166x + 2200 \:=\:0$

The Quadratic Formula gives us: .$\displaystyle x \;=\;83 \pm3\sqrt{521}$

The smaller root is the answer: .$\displaystyle x \;=\;83 - 3\sqrt{521} \;\approx\;14.52$ cm.

• Aug 13th 2008, 09:02 AM
masters
Quote:

Originally Posted by Soroban
Hello, Moo!

The stripes comprising the cross can be "moved" to the edges of the flag.
Let $\displaystyle x$ = width of the stripe (cm).
Code:

              100       * - - - - - - - - *       |                | x       |  * - - - - - - *   66 |  |            |       |  |            | 66-x       |  |            |       * - * - - - - - - *         x      100-x

The blue region's area is: .$\displaystyle \frac{2}{3} \times (66\cdot100) \:=\;4400$ cm²

It is also: .$\displaystyle (100-x)(66-x)$ cm²

Hence, we have: .$\displaystyle (100-x)(66-x) \:=\:4400 \quad\Rightarrow\quad x^2 - 166x + 2200 \:=\:0$

The Quadratic Formula gives us: .$\displaystyle x \;=\;83 \pm3\sqrt{521}$

The smaller root is the answer: .$\displaystyle x \;=\;83 - 3\sqrt{521} \;\approx\;14.52$ cm.

See Post 10 for a different approach which yields the same result.
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