Nostalgia

[simont]

Trying to recapture your childhood is always dangerous. Books you read, games you played and TV you watched as a child are all things you can dig out and read, play or watch again; sometimes they'll be as good as you remember, but often they won't.

Usually that's because you have changed, of course; but not in this case. This month I remembered a game my father taught me some time around my late teens: you take the four digits of the current year, and you attempt to combine them arithmetically to form each number from 1 upwards and see how far you can get. You're allowed to add, subtract, multiply and divide, you're allowed to use parentheses (of course), and you're also allowed to start by concatenating some of the digits into larger numbers if you want. The catch is that you have to use all four digits every time; if one or two of them can easily be combined to produce the target you're after, you have to find a way to safely dispose of the others. The next year, you can start all over again and it'll all be completely different.

So in 1992, for example, I might have started with 1=2-1+9-9 and 2=1+2-9/9, got as far as 22=21+9/9, and had trouble with 23. It needn't stop there, of course; I might have skipped 23 and tried for things above that.

Like so many things one remembers fondly from one's childhood, this game is not as much fun as I remember it being; but this time it isn't me who's changed. When two of the digits of the current year are zeroes, it gets very boring! If anyone is contemplating having a go at this game, I urge them to wait until at least 2011; and I don't think the game will really recover all of its fun until some time around 2134.

Comments

[cartesiandaemon.livejournal.com]

True, but you *didn't*. If you're similar to me, at one point, your first thought was "Ooh, this is fun" and at a later point your first thought is "This is a solved problem. How do I find the general answer with a formula or computer again?"

Both are equally interesting reactions, because the first leads to the second, whilest often *doing* the first leads to more understanding (eg. suggestions for similar games/theorems), but it shows a change in view.

Or am I bullshitting? :)

[simont]

Actually, my primary purpose in writing a solver is to turn it round and use it for generation: my hope is that I'll be able to invent puzzles of this type with vaguely consistent difficulty.

(There are two particularly good ones I know of: try making 24 using 3,3,8,8, and then try making 1 using 1,1,1,5. In both these cases you aren't allowed digit concatenation, and you must use all the numbers.)

[shadowphiar.livejournal.com]

Are those puzzles using the restricted rules, or am I allowed to invoke wacky operators?

[simont]

The two I just mentioned? No wacky operators needed there. Addition, subtraction, multiplication and division only. Evaluation order is unrestricted (i.e. use as many parentheses as you like). No digit concatenation: the four inputs must be used as separate numbers and combined only by arithmetic operations.

[cartesiandaemon.livejournal.com]

Gaaah! I thought "I won't download any excecutables or source, that should keep be safe from simon's insiduous puzzles..." but no, apparently *talking* to you is enough to ruin my productivity :)

I know I've solved the 1115 thing *before*, but totally mind-blanked, and wrote a perl script to try all combinations. Doh!

[ewx.livejournal.com]

1 from 1115 I got reasonably quickly when it came up one evening. 24 from 3388 I'm still thinking on...