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.
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 $1, 3, 5, 15$.
If $p$ is the perimeter of a right angle triangle with integral length sides, $\{a, b, c\}$, there are exactly three such triangles for $p = 120$:
$\{20,48,52\}$, $\{24,45,51\}$, $\{30,40,50\}$
For which value of $p \le 1000$, is the number of such triangles maximised?
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!
Given a string s
, write a function to find the length of the longest substring without repeating characters.
No nesting of for-loops allowed!