I made it up to use for a driving game - just something to pass the time if I'm driving somewhere on country roads. You look at the numbers for addresses as you drive by and try to solve it. Today was the first time I tried to explain the game to someone else. Now it has a bit of a new purpose. So, here's how it works.
Take any 4 digit number without a zero, and separate those digits into their 4 separate 1-9 values. Find a way to mathematically (in any arrangement), reduce those numbers to 1.
Some examples:
Starting number: 9743
9 - 7 + 3 - 4
9 - 7 = 2
2 + 3 = 5
5 - 4 = 1
Starting number: 9871
(9 + 7) / 8 - 1
9 + 7 = 16
16 / 8 = 2
2 - 1 = 1
Starting number: 2435
(5 - 4) x (3 - 2)
5 - 4 = 1
3 - 2 = 1
1 x 1 = 1
The most difficult starting number I've come up with is 9861 (hint: think exponentially). I haven't come up with any combinations that can't be solved.
Monday, April 23, 2007
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4 comments:
That's cool AJ. You should try solving for other numbers next. I can't think of any combos that can't be solved for 1 either.
Also, solving 3 numbers for 1 and then using the last number as an exponent for 1 feels like a chess game with my younger brother - it's too easy.. How about: 9861 use sq rt of 9 to solve. Multiplying by one at the end kinda makes me feel cheap too though. Watch the road... JP
Sorry JP, no dice. If you were going to square root something, you'd need a 2 (just like if you were going to cube root, you'd need a 3). You can't just go around willy-nilly applying effects for fun. I mean, why not just take 6 to the second power, divide by 9, divide 8 by that result, and subtract 1? You have to get your numbers from somewhere! The square root symbol has an invisible two on it.
In other words...check - watch your king.
Evidently the chess analogy was very accurate. There isn't a two on any square root sign I've ever seen. But if you want to take back a move, go ahead. I'll play 9 minus the mean of 8 and 6 minus 1 equals 1. Checkmate.
Very nice. For the record, my solution was 9 - 6 = 3. Use the 3 to get the cube root of 8 = 2. 2 - 1 = 1.
The only way I've found to solve 9841 is by being "cheap". Maybe you have some "out of the box" solution for that one (I'd never really considered 'mean/average' in my numbers game, but I suppose it's OK).
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