Puzzles

Problems to exhibit and strengthen your J muscles. In the Wiki spirit, the solutions are intended to be community efforts, and the solution pages slates on which to record your answers and observations.

• Find an interesting use of the monad *./ on a list of integers with length greater

than 2. Solution

• Find a tacit expression that computes f y if y is greater than 1,

otherwise just return y . Solution

• Given a list of integers, set each item that is less than n1 to n2 .

Can it be expressed without an explicit loop? Solution

• Find examples of "under". Solution
• What are some ways of computing the i-th Fibonacci number? Solution
• What are some ways of computing the sine of a number? Solution
• Puzzle of the year 2005: find phrases that generate each number i.100 .  Solution
• Puzzle of the year 2006: find phrases that generate each number i.100 .  Solution
• Puzzle of the year 2007: find phrases that generate each number i.100 .  Solution
• Puzzle of the year 2008: find phrases that generate each number i.100 .  Solution
• Puzzle of the year 2009: find phrases that generate each number i.100 .  Solution
• Puzzle of the year 2010: find phrases that generate each number i.100 .  Solution
• N Queens Problem: Place n queens on an (n,n) chessboard so that none attacks another. Solution
• Queens and Knights: Place an equal number of queens and knights on an (8,8) chessboard so that none attacks another. What is the maximum number of pieces you can so place, and how many different ways can you do it? Solution
• Find the sum of all the integers between 1 and 10^11 that are both divisible by seven and, when the decimal digits are reversed, are still divisible by seven. Solution
• Find a palindromic pangram. Solution
• Fill the zero gaps in a list using linear interpolation. Solution
• Find permutations such that adjacent numbers form a base-10 number not divisible by 3, 4, or 5. Solution
• Find a 9-digit number $a_{1}a_{2}\dots a_{9}$ containing all the digits 1,2,...,9 such that $k$ divides $a_{1}a_{2}\dots a_{k}$ for each $k=1,2,\dots 9$. Solution
• Find k-digit numbers m such that all n-digit prefixes of m are divisible by n . Solution
• Find shortest and/or smartest phrase to build ASCII art I. Solution
• Find shortest and/or smartest phrase to build ASCII art II. Solution
• Another ASCII art puzzle: draw the complete binary tree of order n . Solution
• Instruct a human to sort a list, in the easiest possible way. Solution
• Create a non-trivial J quine, program script that prints itself. Solution
• APL Idioms puzzle from Vector 21.4. Solution
• Arrange a list of distinct positive integers so that no two numbers have their average between them. Solution
• How many ways can a unit fraction 1%n be expressed as a sum of unit fractions 1%x and 1%y ? Solution
• Given a list of words, find the top m most frequent words and the corresponding frequencies. Solution
• Find an expression for a sequence of exponents using subtraction as the only numeric operation. Solution
• Provide a sentence whose result is 2147483647. Constraints apply and are given on the solution page. Solution
• Provide a sentence whose result is 340282366920938463463374607431768211455. Constraints apply and are given on the solution page. Solution
• Provide a query which causes Google to return a J Dictionary page in the top 3 search results. Constraints apply and are given on the solution page. Solution
• Given a short J phrase, provide the equivalent common English idiom. Solution
• Generate the first 2^n gray codes. Solution
• Given a primitive p from the Vocabulary, define it in terms of other primitives. Solution
• Find interesting equivalents of +/@i. Solution
• Under what conditions is it true that (x i. y) -: (~.x) i. y ? Solution
• Find the sum of a non-empty numeric vector v without using the character + . Solution
• Determine all the times whose display on a 24-hour clock is prime Solution
• Compress the decimal representation of a natural number. Solutions
• Implement mergesort making a maximal use of J array-oriented features Solution