Zin Obelisk
In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.
Age
11 to 14
Challenge level
Problem
In the ancient city of Atlantis a monument called a Zin Obelisk was built in honour of the goddess Tina.
The structure (a cuboid) took less than two weeks to complete.
Your task is to determine on which day of the week the monument was completed.
You will need a set of information cards to solve the problem.
For the set, you'll need to print off this Word document or this pdf.
Printable NRICH Roadshow resource.
Image
The original version of this problem appeared in "Improving Work Groups: A Practical Manual for Team Building" by Dave Francis & Don Young.
Getting Started
Try to group the information to make it more manageable.
Student Solutions
We had a number of correct solutions including some from students from Our Lady's G.S. Newry, several from students from Marist College in New Zealand (Kate and Lauren, Aimee and Hannah, Jessica and Alesha, Helen and Maiya), Ben, Alex, Rob and Harry from the Royal Latin School, Niall, Tyler, Daniele, Michael and Thomas from St.Margarets C.E.Primary School, Ben, Beth, Caitlin, Connor H, Connor L, Flora and Harry from Maynards Green Primary School, Kai, Harry and William from Herbert Strutt School, Bandhagi from The Garden International School and Charlotte, China, Kyle, Viva, Dannielle, Jordan and Emily, all from Kavanagh College.
The Maths Challenge Group from Colyton Grammar School sent a very clear explanation of how they arrived at the correct result:
As a start, we organised the cards into categories:
Facts about the obelisk
Facts about time measurementFacts about workers
We also found that there were a number of cards that were irrelevant to the solution.
Given the dimensions of the obelisk, we found that its volume is 100 x 50 x 10 = 50,000 cubic feet.
As each block is 1 cubic foot, this would require 50,000 blocks to make.
As the group size was 9, but one could not work, 8 people would be working on the obelisk.
In addition, as the day was nine schlibs long, but the workers rest for sixteen ponks (which equates to two schlibs), each worker would be building for seven schlibs a day.
They would each be able to lay 150 blocks per schlib, and per day this is 150 x 7 = 1050.
The whole group would therefore be able to lay 1050 x 8 = 8400 blocks a day.
Consequently, the obelisk would take a total of six days to complete, as in six days they could lay 8400 x 6 = 50,400 blocks (in five days this total would only be 42,000 blocks).
The Atlantian week has 5 days but only 4 of those would be spent working, so the work would be completed on the 2nd day of the 2nd week, which is Neptiminus.
Very similar thinking was used by Karim from Wilson's School:
1. The dimensions of the zin indicate that it contains 50,000 cubic feet of stone blocks.2. The blocks are 1 cubic foot each, therefore, 50,000 blocks are required.
3. Each worker works 7 schlibs in a day (2 schlibs are devoted to rest).
4. Each worker lays 150 blocks per schlib, therefore each worker lays 1050 blocks per day.
5. There are 8 workers per day, therefore 8,400 blocks are laid per working day.
6. The 50,000th block, therefore, is laid on the sixth working day.
7. Since work does not take place on Daydoldrum, the sixth working day is Neptiminus.
Here is Mark's clearly laid out solution.
Edwin, Aufar, Hyeon and Dylan from B.S.M Muscat in Oman also found out that they finished building the Obelisk on Neptiminus. They added:
This puzzle was amazing!Glad you enjoyed it. Well done to you all.
Teachers' Resources
Why do this problem?
This problem challenges students to make sense of a lot of random information and to apply their knowledge of proportionality and measures to answer the question.Possible approach
This is an ideal activity for students to carry out in small groups of 3 or 4. Some groups work better when its members have been allocated clear roles. A handout detailing possible roles that has been used successfully by some schools is available as a Word document or in pdf format.
Print and cut out sets of cards with the information and distribute to members of each group (they are available here as Word documents on in pdf format ).
The task for each "team" is to determine on which day of the week the obelisk was completed. There may be some disagreement between the groups so let them know that they will be expected to justify their answers.
Each group could be asked to set out their working/justifications on a large sheet of flipchart paper before being asked to talk to the whole class. How did they group the information to make it more manageable? How did they decide that some of the information was unnecessary?
Each group could be asked to set out their working/justifications on a large sheet of flipchart paper before being asked to talk to the whole class. How did they group the information to make it more manageable? How did they decide that some of the information was unnecessary?
Key questions
What behaviour helped the group accomplish the task?
What behaviour hindered the group in completing the task?
How did leadership emerge in the team?
Who participated most? Who participated least?
What feelings did you experience as the task progressed?
What suggestions would you make to improve team performance?
Possible extension
A possibly more difficult problem that again requires students to draw conclusions from information is Nutrition and Cycling.Possible support
Possible ways to simplify the problem could involve:
- offering students the information in an organised form
- removing information that is not required.