Problem Comparing two numbers written in index form like 211 and 37 is not difficult, as any calculator would confirm that 211 = 2048 < 37 = 2187. However, confirming that 632382518061 > 519432525806 would be much more difficult, as both numbers contain over three million digits. Using base_exp.txt (right click and ‘Save Link/Target As…’), …
In my last post I explained the difference between the techniques of Currying and Partial Application, following on where there let me show you how you might apply these two techniques in F#, Javascript and C#. F# Starting with F#, being a functional language it makes currying and partial application dead easy (considering that they …
Currying and Partial Applications in F#, Javascript and C# Read More »
Recently I have come across some really interesting questions and debates around these two terms and how they differ from one another. There seems to be widespread confusions with many examples demonstrates one whilst intends another, and some simply uses the terms interchangeably. Whilst admittedly not being a function programming expert, I’ve spent a bit …
Problem In the card game poker, a hand consists of five cards and are ranked, from lowest to highest, in the following way: High Card: Highest value card. One Pair: Two cards of the same value. Two Pairs: Two different pairs. Three of a Kind: Three cards of the same value. Straight: All cards are …
Problem The rules for writing Roman numerals allow for many ways of writing each number (see FAQ:Roman Numerals). However, there is always a “best” way of writing a particular number. For example, the following represent all of the legitimate ways of writing the number sixteen: IIIIIIIIIIIIIIII VIIIIIIIIIII VVIIIIII XIIIIII VVVI XVI The last example being …
Problem Consider quadratic Diophantine equations of the form: x2 – Dy2 = 1 For example, when D=13, the minimal solution in x is 6492 – 13×1802 = 1. It can be assumed that there are no solutions in positive integers when D is square. By finding minimal solutions in x for D = {2, 3, …
Problem Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can separated into piles in exactly seven different ways, so p(5)=7. OOOOO OOOO O OOO OO OOO O O OO OO O OO O O O O O O O O Find the …
Problem It is possible to write ten as the sum of primes in exactly five different ways: 7 + 3 5 + 5 5 + 3 + 2 3 + 3 + 2 + 2 2 + 2 + 2 + 2 + 2 What is the first value which can be written as the …
Problem It is possible to write five as a sum in exactly six different ways: 4 + 1 3 + 2 3 + 1 + 1 2 + 2 + 1 2 + 1 + 1 + 1 1 + 1 + 1 + 1 + 1 How many different ways can one hundred be …
Problem The 5-digit number, 16807=75, is also a fifth power. Similarly, the 9-digit number, 134217728=89, is a ninth power. How many n-digit positive integers exist which are also an nth power? Solution
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