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TASK #1 - Pythagorean Means
You are given a set of integers.
Write a script to compute all three Pythagorean Means i.e Arithmetic Mean,
Geometric Mean and Harmonic Mean of the given set of integers. Please
refer to wikipedia page for more informations.
Example 1:
Input: @n = (1,3,5,6,9)
Output: AM = 4.8, GM = 3.9, HM = 2.8
Example 2:
Input: @n = (2,4,6,8,10)
Output: AM = 6.0, GM = 5.2, HM = 4.4
Example 3:
Input: @n = (1,2,3,4,5)
Output: AM = 3.0, GM = 2.6, HM = 2.2
MY NOTES: ok. Pretty easy, although the geometric mean involves
calculating the product of the numbers, which may get pretty huge.
Tried bigrat, but it broke the nth-root calculation using **.
TASK #2 - Brazilian Number
You are given a number $n > 3.
Write a script to find out if the given number is a Brazilian Number.
A positive integer number N has at least one natural number B where
1 < B < N-1 where the representation of N in base B has same digits.
Example 1:
Input: $n = 7
Output: 1
Since 7 in base 2 is 111.
Example 2:
Input: $n = 6
Output: 0
Since 6 in base 2 is 110,
6 in base 3 is 20 and
6 in base 4 is 12.
Example 3:
Input: $n = 8
Output: 1
Since 8 in base 3 is 22.
MY NOTES: ok, so "same digits" really means "the same base-b digit
repeated throughout the entire string". Sounds pretty easy.
Added debugging mode to produce and display the "Since" messages,
formatted nicely. Then added tabulate mode to show the first N
Brazilian numbers (this interoperates nicely with -d).
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