# Scouts in Boats

##### Level 1Level 2Level 3Level 4More Puzzles

Day 1

0

0

0

0

0

0

Day 2

0

0

0

0

0

0

Day 3

0

0

0

0

0

0

Day 4

0

0

0

0

0

0

Day 5

0

0

0

0

0

0

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.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

## More Activities:

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 9 October 'Starter of the Day' page by Mr Jones, Wales:

"I think that having a starter of the day helps improve maths in general. My pupils say they love them!!!"

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

#### Car Park Puzzle

Can you get your car out of the very crowded car park by moving other cars forwards or backwards? There are five levels of increasing difficulty and the interactive interface makes this a fun problem solving exercise.

## Numeracy

"Numeracy is a proficiency which is developed mainly in Mathematics but also in other subjects. It is more than an ability to do basic arithmetic. It involves developing confidence and competence with numbers and measures. It requires understanding of the number system, a repertoire of mathematical techniques, and an inclination and ability to solve quantitative or spatial problems in a range of contexts. Numeracy also demands understanding of the ways in which data are gathered by counting and measuring, and presented in graphs, diagrams, charts and tables."

Secondary National Strategy, Mathematics at key stage 3

## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

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 Ă‰tienne or Ĺ˝eljko.
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!"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

For All: