Shortest Path Sum

Given the hex string in the white box below. Construct a graph according to the following rules:

• Each unique letter is a node.
• Two nodes have an edge between them if they are adjacent in the string.
• The weight of the edge between two nodes is the hex value of the two connected nodes.
• If the same edge appears twice, ignore its second appearance.
• The weight of an edge from a node to itself is zero.

Find the sum of every unique shortest path. Two shortest paths are unique if one of the paths contains at least one node that the other does not. The shortest path between two nodes is a series of edges along which one could travel to get from one node to the other.

Binary Search

Given the function below, find the largest integer n such that query(n) returns false and query(n+1) returns true. The answer is an integer between 1 and 80000000000 (80 billion!)

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14

function query(n) {
    let d1 = dist(n);
    let d2 = dist(n + 1);
    return d2 > d1;
}
function dist(v) {
    let c = (v + 28000000000)/10000000000;
    let t = c * Math.log(c)/2;
    let a = Math.pow(t - c, 2);
    let b1 = t + c;
    let b2 = c * Math.log(c);
    let b = Math.pow(b1 - b2, 2);
    return Math.sqrt(a + b);
}

Odd and Even Numbers 😏

Find the missing value (hint: read the title):

• 80618 = 4
• 10792 = 2
• 21643 = 3
• 75335 = 0
• 44713 = ?