Same Five Digits

Enigma is a weekly column in New Scientist.  Every week it has a new puzzle.  Some of the Enigma puzzles could be solved using a computer.

This week’s puzzle, Enigma number 1638, is in that category.  Here are the facts of the problem.

• I am thinking of three numbers.
• Each number is a perfect square.
• Each number has five digits.
• Five different digits occur in all three numbers.
• Each of the five digits occurs a different number of times.
• The five numbers of times is the same as the five digits.
• No digit occurs its own number of times.  (E.g., 4 is not used 4 times.)
• If you knew which digit occurs once, you could uniquely identify the numbers.

Your task is to write a program that finds and prints the three perfect squares I am thinking of.

Reading List

I’ve been doing some reading this weekend.  This post records a little of what I’ve learned.

The focus has been Scheme macros and separate compilation.  I’m trying to understand how a production quality Scheme system “should” be organized.  “Should” is in scare quotes because every Scheme user has at least one opinion on the topic, and no two seem to agree.

So here are the papers I’ve looked at in the last few days.

A Safer Scheme Interpreter, Part 3

In Part 1, I explained why my Scheme interpreter, Schetoo, has the ability to fail or restart any instruction.  In Part 2, I showed how it automatically checks that instructions do all necessary checks before they have any side effects.  Those two posts described raising exceptions with longjmp, but didn’t really explain how the interpreter catches exceptions.

A Safer Scheme Interpreter, Part 2

In my last post, I promised to explain how my Scheme interpreter, Schetoo, can automatically verify that its instructions are restartable.  But first, some background.

A Safer Scheme Interpreter

In the first half of 2010, I wrote a Scheme interpreter which I called Schetoo. It is a sequel to an interpreter called kbscheme, which I worked on off-and-on in 2008 and 2009. Both are written in C.

You can see them both on github.

https://github.com/kbob/kbscheme
https://github.com/kbob/schetoo

I undertook these projects to learn more about Scheme, interpreters, and garbage collection. Along the way, I came up with an interesting technique to make interpreter implementation less error-prone. That’s what I want to write about today.

Variadic functions in C: a new idiom?

For a long time, C has let you write functions that take a variable number of arguments.  But C leaves it up to each variadic function to figure out how many arguments it’s been passed, and up to each caller to pass the right arguments.

Here’s a cute hack to make variadic functions easier to write and a little harder to call incorrectly.

Son of Scheme: Introducing Schetoo

I’ve started a new Scheme project. This one is called Schetoo. The name has connotations of “Scheme Two”, “me too”, and “Gentoo” (a hardcore Linux distribution and a breed of penguin).

A ‘blogger named Peter Michaux started a series in January called Scheme from Scratch. His goal was to write a very quick and dirty Scheme, just enough to bootstrap a Scheme compiler. I read his postings and decided to get started again.

Schetoo is similar in concept to my first Scheme, kbscheme. In fact, I reused a fair amount of code to get Schetoo up and running faster. But at the same time, I’m applying what I learned to try to get a better design.

I’ve published the code on GitHub.

http://github.com/kbob/schetoo

Mac Mini Video Upgrade

I recently upgraded our Mac Mini media center with a new video decoder board. Surprisingly, it worked.

Scheme from Scratch

Peter Michaux has started a ‘blog series called Scheme from Scratch. He’s made ten posts so far. He’s developing a Scheme system incrementally, in tiny steps, so that it’s easy to read along and understand exactly what every bit of code does.

Recommended.

Scheme: Retrospective

The Scheme interpreter project is “on hold”. Maybe it’s “finished”. It’s time to take stock, see what I learned, what I accomplished, and what I could have done better.