# tortoise and hare?

12 views

### John Hanna

Jan 31, 2022, 12:25:25 PMJan 31

Greetings, folks,

I’ve been working on a ‘tortoise and hare’ race. The slow but steady tortoise moves randint(1, 9) units every tick. The fast but lazy hare hops randint(a, b) steps every 10 ticks.  What values of a and b produce a ‘fair’ race where each wins about half the time?

The race is 300 units and the first tick is 1, not 0.

Does it matter if, at each tick, the tortoise goes first or should that be ‘fair’ (even chance of either going first) as well? The hare move 0 units 9/10 ticks.

Thanks, and

Be kind,

John

### Landy Godbold

Jan 31, 2022, 8:06:44 PMJan 31
John:

I will not answer this one until I have a bit of time to think about it some (but I'm pretty sure there is not a unique (a, b) pair that does the trick).

The real reason for this note is to ask your permission to re-post your question to the AP Stats list (or ask YOU to post it there ).  Since probability and expected value are required topics in that course this might be a fun problem for students to look at, either now or after the AP exam.

cheers,
Landy

Sent: Monday, January 31, 2022 12:25 PM
Subject: [tinspire] tortoise and hare?

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### John Hanna

Jan 31, 2022, 10:09:52 PMJan 31

### krogi us

Feb 1, 2022, 7:06:25 PMFeb 1
to tinspire
Here is the solution disney knows.

### John Hanna

Feb 1, 2022, 10:23:56 PMFeb 1

Thanks! You’ve given me names!

### Jody Crothers

Feb 2, 2022, 5:50:42 AMFeb 2
Hi John

This would be great to code for the Rover so they can see the race.

Jody Crothers

Ridge View Secondary College

Western Australia

Sent: Wednesday, 2 February 2022 11:23 AM
Subject: RE: [tinspire] tortoise and hare?

### John Hanna

Feb 2, 2022, 7:04:17 AMFeb 2

That would be quite different since there are two cpu’s at work.

Anyone set up a Rover race track like Olympus Mons project?

### Jody Crothers

Feb 2, 2022, 7:24:33 AMFeb 2
I did one with a coin toss with 2 rovers and dice rolling with 6 rovers, I just used the same randseed to start in each rover.

Jody Crothers