#!/usr/bin/env python
# coding: utf-8

# ## Challenges

# ### Exercise
# 
# Starting with the number and moving to the right in a clockwise direction a by
# 
# spiral is formed as follows:
#     
# ```
# 21 22 23 24 25
# 20  7  8  9 10
# 19  6  1  2 11
# 18  5  4  3 12
# 17 16 15 14 13
# ```
# 
# It can be verified that the sum of the numbers on the diagonals is 21+7+1+3+13+25+9+5+17=101.
# 
# What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
# 
# Hint: You do not need to compute this spiral, just take a close look at the numbers that are summed up.

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# ### Exercise
# 
# <p>Find the number of integers $1 \lt n \lt 10^7$, for which $n$ and $n + 1$ have the same number of positive divisors. For example, $14$ has the positive divisors $1, 2, 7, 14$ while $15$ has $1, 3, 5, 15$.</p>

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# ### Exercise
# 
# <p>If $p$ is the perimeter of a right angle triangle with integral length sides, $\{a, b, c\}$, there are exactly three such triangles for $p = 120$:</p>
# <p>$\{20,48,52\}$, $\{24,45,51\}$, $\{30,40,50\}$</p>
# <p>For which value of $p \le 1000$, is the number of such triangles maximised?</p>

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# ### Exercise
# 
# Given two sorted lists, write a function to merge these lists into a new sorted list.
# 
# Example: `[1,2,5,6,6,7]` and `[2,3,8]` --> `[1,2,2,3,5,6,6,7,8]`
# 
# No nesting of loops allowed!

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# ### Exercise
# 
# Given a string `s`, write a function to find the length of the longest substring without repeating characters.
# 
# No nesting of for-loops allowed!

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