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Snail Race, Part 2 (December 2023 Challenge Question)

Posted November 30, 2023 12:00 AM
Pathfinder Tags: challenge question

After the fervor of last month, you are all in on snail racing.

In fact you now own 25 racing snails. But now you need to identify the 3 fastest snails.

Your snail race track has 5 equal racing lanes. But the timer doesn't have enough digits to show the elapsed time of the snails.

What is the minimum number of races required to identify the 3 fastest snails? How do you organize them?

(Bonus: Good answers awarded to snail puns and creative snail names.)

Answer (12.21.23)

7 races

  • 5 qualifying races of 5 snails each
  • 1 winners race
    • Get fastest snail overall
    • Eliminates
      • Snails #4 and #5 from top 3 fastest snails
      • All snails that lost to snails #3, #4 and #5 too.
    • But there are three snails who lack direct comparisons.
      • The 2nd and 3rd place snails that finished behind the overall fastest snail in qualifying.
      • The snail from qualifying that finished behind the winners' race #2 snail.
  • 1 place race
    • Second and third place from the overall winners' first race
    • Second and third place from the overall winners' qualifying race.
    • Snail from qualifying that finished behind the winners' race #2 snail..
    • Get second and third fastest overall
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Guru

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#1

Re: Snail Race, Part 2 (December 2023 Challenge Question)

11/30/2023 9:41 AM

Here's a first stab at it. If you put 5 in a race, the 2 slowest ones cannot be one of the fastest 3.

First 5 races, eliminate bottom 2 from each, 10 in all, leaving 15.

Race remaining 15 (3 races) eliminating slowest 2 in each race, leaving 9 potential winners.

Pick 5 of the 9, race them, eliminate slowest 2, leaving 7.

Pick 5 of the 7, race them, eliminate slowest 2, leaving 5.

Race final 5, top 3 are the winners.

Total of 11 races.

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#2

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/02/2023 8:48 PM

The statement "But the timer doesn't have enough digits to show the elapsed time of the snails" seems to be saying that there is no way to declare the winner of a race. If my observation is correct, then there is no answer. There can be no competition without better timer equipment, a shorter track, or the ability to have human observation declare race winners.

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#3
In reply to #2

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/03/2023 6:51 AM

I'm thinking it means that you cannot just run the snails 5 at a time and record the times for each. That would only require 5 races and a sorting algorithm.

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4
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#4

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 7:27 AM

Wow, late to this party, but, no decent answers yet.

First if the racers were white horses they would have to be named after stars (like those in Ben-Hur), but, as we are dealing with such wild and dynamic beasts I think they should be named after the 23/24 storms:

Agnes, Babet, Ciaran, Debi, Elin, Fergus, Gerrit, Henk, Isha, Jocelyn, Kathleen, Lilian, Minnie, Nicholas, Olga, Piet, Regina, Stuart, Tamiko, Vincent and Walid.

I'll have to add: Quentin, Ulysses, Xavier and Yolanda to get to 25.

First five races

ABCDE

FGHIJ

KLMNO

PQRST

UVWXY

Suppose without loss of generality that they arrive in the orders shown.

sixth race:

AFKPU

Again WLOG suppose they arrive in that order.

P and U are out, and, therefore clearly so are Q and V. With a little more thought it's also clear that L is out

Seventh race

FKBCG

And the fastest two from this race join A as the fastest three.

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#5
In reply to #4

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 8:40 AM

Very clever. I followed you until "also clear that L is out". Please elaborate...

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#6
In reply to #5

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 9:06 AM

K is the third fastest of AF and K, and L is slower than K (from the third race).

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#8
In reply to #6

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 10:56 AM

Thanks, obvious, now.

GA

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#12
In reply to #5

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/05/2023 8:57 AM

It’s a Christmas pun - no L (Noel) Ha!

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#7
In reply to #4

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 10:54 AM

Each race, eliminate slowest 2.

#1 A B C D E

#2 F G H I J

#3 K L M N O

#4 P Q R S T

#5 U V W X Y

#6 A F K P U

If P and U are eliminated (race#6), so are Q, R (beaten by P, race#4) and V, W (beaten by U, race#5). K is, at best, in 3rd place (race#6), so eliminate L and M (race#3).

Last race (#7), K versus B, C, G, and H, winner is third place.

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#9
In reply to #7

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 11:54 AM

Last race (#7), K versus B, C, G, and H, winner is third place.

No the Last race has to be

Last race (#7), K versus B, C, G, and F. First and second are second and third fastest.

(A is the fastest: If F and G are next then H is not a contender, but, A/B/C is still a possibility.)

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#10
In reply to #9

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/04/2023 8:38 PM

You are correct. Thanks.

This was an interesting puzzle

Red = eliminated snails, Races # 1 - 6

Race #7 K F G B C

Winners are either ABC or AFK

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#11
In reply to #10

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/05/2023 7:56 AM

Or ABF or ABG

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#19
In reply to #10

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/20/2023 2:30 AM

Good answer

possible finishes

A B C

A B F

A F B

A F G

A F K

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#18
In reply to #7

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/20/2023 2:09 AM

B and C could still be faster than F. You need one more race.

edit

I should have read the other answers before replying

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#17
In reply to #4

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/20/2023 2:02 AM

There is a fault in your logic. What if just by chance ABC in the same heat are the three fastest overall?

The correct answer is at most eight heats can pick the three fastest.

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#20
In reply to #4

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/21/2023 9:27 AM

Beautiful.

Not only did you name the snails, you determine which 3 are fastest in minimum number of races (7).

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#13

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/12/2023 5:54 PM

Who's a good boy??

We will literally crush the competition...!!

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#14
In reply to #13

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/17/2023 3:57 AM

Excellent...

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#15

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/18/2023 3:58 PM

Is drafting allowed,with more than one snail per track?

Is passing or over running over a slower snail on same track permitted?

How about bumping another snail off the track?

Must each snail stay in one track only?

Is a snail allowed to modify his slime for lower viscosity and friction to gain an edge over the competition?

Are snails allowed to lower their shells for better ground effect?

Are all snails tested for drugs?

Can their shells be polished for less wind resistance and higher speed?

Are slugs allowed to enter this race?

What if a slug identifies himself/herself/itself as a snail?

Assume nothing.Verify everything.

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#16
In reply to #15

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/19/2023 5:35 AM

Here is a partial list of snail names:

Snailer Swift

Speedy

Slimeball

Escar-go

Snaily Cyrus

Gooey

Slowpoke

Snailen

Shelebrity

Contrail

Avoid fast food...eat snails.

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#21
In reply to #16

Re: Snail Race, Part 2 (December 2023 Challenge Question)

12/21/2023 9:29 AM

Very punny! Thanks for the effort. GA.

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#22

Re: Snail Race, Part 2 (December 2023 Challenge Question)

02/15/2024 6:19 AM

In an attempt to speed up one snail, I removed its shell.
It just made it sluggish....
Del

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