Problem By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom in triangle.txt (right click and ‘Save Link/Target …
Problem By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: NOTE: As …
Problem The Fibonacci sequence is defined by the recurrence relation: Fn = Fn-1 + Fn-2, where F1 = 1 and F2 = 1. Hence the first 12 terms will be: F1 = 1 F2 = 1 F3 = 2 F4 = 3 F5 = 5 F6 = 8 F7 = 13 F8 = 21 F9 …
Problem If the numbers 1 to 5 are written out in words: one, two, three, four, five, then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total. If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would …
Problem Starting in the top left corner of a 2×2 grid, there are 6 routes (without backtracking) to the bottom right corner. How many routes are there through a 20×20 grid? Solution It took me a while to figure out that this problem is actually a simple combination problem – consider a X by Y …
Problem The following iterative sequence is defined for the set of positive integers: n –> n/2 (n is even) n –> 3n + 1 (n is odd) Using the rule above and starting with 13, we generate the following sequence: 13 –> 40 –> 20 –> 10 –> 5 –> 16 –> 8 –> 4 …
Problem Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a != b, then a and b are an amicable pair and each of a and b are called amicable numbers. For example, the …
Problem Using names.txt (right click and ‘Save Link/Target As…’), a 46K text file containing over five-thousand first names, begin by sorting it into alphabetical order. Then working out the alphabetical value for each name, multiply this value by its alphabetical position in the list to obtain a name score. For example, when the list is …
Problem n! means n x (n – 1) x … x 3 x 2 x 1 Find the sum of the digits in the number 100! Solution This solution is pretty straight forward, though you might be curious as to what the rec keyword in the factorial function is for. In F# you need to …
Problem 215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. What is the sum of the digits of the number 21000? Solution
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