X-Test Solutions, Part 3!!

X-Test Part 3: SOLUTIONS!!

1) What is the “green area”/“red area” ratio? (You can use only simple math)

(All the 5 medium size circles are equals and they are inscripted in the BIG one, the same for the smaller circles inscripted in the medium circles)

( First we can notice 2 times the sum of the red areas is equal to the middle circle’s area subtracted the area of the six circle inside..

You know that (if “r” is equal to the range of the central circle) the ranges of the two internal circles are r/2. If we call “x” the range of one of the smallest circles, we can use the Pytagora’s theorem:

(r/2+x)^2-(r/2-x)^2=(r-x)^2-x^2. This means x=r/4.

We can know the red area: it is RED=pi*r^2-2*[pi(r/2)^2+2*pi*r^2]=1/8*(pi*r^2)

The area of the BIG circle is W=(pi*(3r)^2)=9*pi*r^2, so the green area is GREEN=1/4*(W-5*pi*r^2)=(1/4*4) *pi*r^2=pi*r^2 (the green area is equal to the area of one of the r range circles).

The asked ratio is: GREEN/RED=(pi*r^2)/[1/8*(pi*r^2]=8 ).

2) Draw this shape: 521478963    (it is a (square) SPIRAL on the calculator)

3) Discover the hidden word: 7412-74123698-987412365-741-87412  (LOGIC – using the same table as above)

4) Decrypt this message

752-845-52-8412-82//  841-781-7-7451-8451       (SUPER SMART– standardized akin-Braille)

5 – UNSOLVED ITEM) Decrypt this message

12-145-125-1235-135-23-125-14-1245-2345-235        (COMPLIMENTS – modified akin-Braille)

6 – UNSOLVED ITEM) Decrypt this message that you are reading on a monitor

11111010-0000XXXX            10101111-000XXXXX       (MORSE CODE – using Morse code, indeed)

P.S.

Item 3 is different between the previous version of the X-Test and the new one:

3- Discover the hidden word:   13825-285-3869-97285    (TILT)