License plate math game

I do lots of things while I ride my bike to work to pass the time. Recently I’ve invented this game (surely others have too):

1. Pick a target integer (I start at zero and move up by one in each iteration)
2. Find a license plate (defined to be one with 3 integers on it like MN has)
3. Find a way to insert mathematical operations before and between the numbers so that the result is your target

Here’s an example: Let’s say your target is 15. Here are a bunch of potential plates:

• 135 (1*3*5)
• 453 (45/3) note that just lumping 2 (or 3) numbers together is allowed
• 771 (7+7+1)
• 241 (2^4-1)

You get the gist.

I have three challenges for you:

1. Find a plate that gives you the most possible targets.
2. Find a plate that gives you the most consecutive targets.
3. Find the target with the most plates that work

Here’s my quick stab at number 2: A plate with “123”:

• Target of 0: -1-2+3
• 1: -1*2+3
• 2: -(1^2)+3
• 3: (1^2)*3
• 4: 12/3
• 5: 1*(2+3)
• 6: 1+2+3
• 7: 1+2*3
• 8: 1*2^3
• 9: (1+2)*3 (or 12-3)

I got stumped trying to do 10.

Can you do better?

Your thoughts? Here are some starters for you:

• I love this. What I do is . . .
• This is dumb. The worst part is . . .
• Do you care if the sign of the answer is correct?
• Why don’t you code this up in Mathematica to figure out 1, 2, and 3?
• Is this what all Provosts do?
• Why don’t you watch the road when you ride?
• Next you’re going to tell me you factor mile marker signs.
• Hey, idiot, here’s how to get 10 with “123”
• Are roots allowed (like 3root8 would be the cube root of 8)?
• I think you shouldn’t be allowed to . . .
• I invented this years ago. Here’s the address to send all the cash you’re going to earn from this blog post . . .