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):

- Pick a target integer (I start at zero and move up by one in each iteration)
- Find a license plate (defined to be one with 3 integers on it like MN has)
- 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:

- Find a plate that gives you the most possible targets.
- Find a plate that gives you the most
*consecutive* targets. - 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 . . .

### Like this:

Like Loading...

*Related*

##
About Andy Rundquist

Professor of physics at Hamline University in St. Paul, MN

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.”

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!