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Arrange the six Scouts in 3 two-person boats so that over the course of the five days they share a boat with all of the other Scouts.
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Richard, Mount Gambier, South Australia
Monday, July 29, 2019
"Hello,
I find the 'Scouts in Boats' puzzles very interesting. So far I have solved level one but I have not yet generalised my method. I think the same approach will work on level 2 but I see a problem with level 3. (In all the Transum pages I have visited, this is only the second problem I have discovered. The first was in Exam-style question 283: trapezium and rectangle.)
I think this puzzle will work as long as the following is true:
S - 1 = (C - 1) * D
where:
S is the number of scouts,
C is the capacity of one boat,
D is the number of days
and S must be a multiple of C.
Level 1:
9 - 1 = (3 - 1) * 4 OK
Level 2:
15 - 1 = (3 - 1) * 7 OK
Level 3:
20 - 1 != (4 - 1) * 5 Not OK!
For level 3, may I suggest:
16 scouts,
4 to a boat,
5 days:
16 - 1 = (4 - 1) * 5 OK
For further levels the numbers could be:
21 scouts,
3 to a boat,
10 days
28 scouts,
4 to a boat,
9 days
25 scouts,
5 to a boat,
6 days.
But then you might need to include names beginning with letters that are not in the English alphabet, such as Étienne or Željko.
Best regards,
Richard."
Transum,
Tuesday, July 30, 2019
"Thanks Richard. You are absolutely right. There was a problem with level 3 so I have removed it for the time being. In actual fact Level 3 was a slightly different puzzle. The wording should have been "Arrange the twenty Scouts in 5 four-person boats so that over the course of the five days they do not share a boat with any Scout they have already shared with." [Note the word NOT in the description]. I now need to find a quiet room to see if your suggested other levels are actually possible then I will update this page.
What would the world be like without people like you Richard? You so kindly take the time to provide the feedback like that above. Thank you so much.
[Update 1st August 2019: I have replaced level 3 with your suggestion]"
Transum,
Thursday, August 1, 2019
"Update: Later on the 1st August 2019 I added a new, easier level and called it level 1. The previous levels 1, 2 and 3 are now levels 2, 3 and 4. This should be noted when reading the comments above that refer to the previous level numbers. All those who have already earned a trophy for this exercise have had the level numbers changed on their trophies in their virtual trophy cabinets!"