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 . . .

About Andy Rundquist

Professor of physics at Hamline University in St. Paul, MN
This entry was posted in fun, math. Bookmark the permalink.

2 Responses to License plate math game

  1. bretbenesh says:

    This trivializes the game, but here is a way to get 10 from “123”:

    10= log_{a}(12) + 3,

    where a=(12)^(1/7).

    It also stretches what we usually mean by “operation.”

    • Andy Rundquist says:

      yeah, that’s probably stretching it a little far 🙂

      Here’s a twitter thread where I was exploring this a little more with python

      Note that targets zero through ~seven have a near 50% chance with any plate!

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