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Press release: April 18, 2011, Periodic Puzzles

Competition Date

Start: Sunday, March 7th, 2010 - 8:00p.m. ET; attachments sent via e-mail

Finish: Friday, March 26th, 5 pm (ET). Completed Puzzles received as attachments.

Periodic Puzzles are chemistry based riddles that use the logic derived from Latin Squares in a competitive environment. Competitors fill in a nine by nine grid in a systematic fashion using element symbols from the periodic table. There are horizontal, vertical, sub-unit (3x3) and alphabetical constraints placed on completing the grid properly. The elements are broken into nine groups based on their chemical/physical properties. As opposed to Sudoku in which nine numbers are used, the Periodic Puzzle completed grid has 81 different elemental symbols.

It is recommended that students have some knowledge of Sudoku puzzles http://www.sudoku.name/

A collaborative effort between the students of the

Other Sponsoring Agencies include the American Chemical Society, the Florida Academy of Science and the Valdosta State University Center for International Programs.

This event is in preparation of the 2011 International Year of Chemistry http://www.chemistry2011.org/

This is a friendly international competition aimed at promoting chemistry, problem solving, and positive group dynamics.

Divisions

(Periodic Coordinator is at: periodic.coordinator@gmail.com).

The answer sheets will only be accepted at the correct division e-mail address.

  1. Middle School Science classes (groups totaling 15 participants accepted)*
    Periodic.MIddle.School@gmail.com

  2. High School (Regular Chemistry and science classes)
    Periodic.high.school@gmail.com

  3. Lower Level Undergraduate (students with no chemistry background or students currently enrolled in General Chemistry; includes High School AP classes
    Periodic.lower.undergrad@gmail.com

  4. Upper Level Undergraduate (students that have completed general chemistry)
    Periodic.upper.undergrad@gmail.com

  5. Open (all ages and backgrounds not included above, from graduate students to retirees).
    6. Periodic.open@gmail.com

Rules


  1. While we would prefer that each group register 48 hours before the competition (March 5th, 3 pm). All must register using the form below. One class can have multiple entries (i.e. a general Chemistry course at a university with 60 students can enter 10 groups of 6). A single group can be from different institutions but the most senior person in the group determines to which division it is allocated.

  2. Each group can have a maximum of six participants (1-6). Only the middle school division can have more (15 maximum).

  3. Institutions can have multiple groups but each group should have an academic advisor.

  4. Below is a document that defines the rules and logistics of the puzzles.

  5. On March 7th, at 8 pm, Eastern Time, participating groups will be (simultaneously) sent 25 puzzles numbered 1-25. These puzzles will be sent as a single WORD document. Both the completed puzzle and the table must be returned as a single attachment.

  6. Puzzles will be returned as attachments in Word (*.doc) format with answered typed (11 pt font, New Times Roman) into the squares (nothing hand written, no .pdf or scanned filed, etc will be accepted).

  7. The puzzles will be numbered 1-25 and must be completed in order.

  8. The competition will start on March 7th and end on March 26th. This will allow teachers to give it as assignments, etc in various classroom settings.

  9. The group that returns the correctly completed puzzles, (all twelve combined in a single file) to the correct e-mail address (above) wins. Late puzzles will not be accepted. Groups are encouraged to submit what they have completed before the dead line.

  10. Each academic group* needs an advisor that will provide a check certifying the completeness of each puzzle. This advisor should not provide leadership or answers during the competition. (*Open participants do not need an advisor).

  11. For international participants in different time zones, we can adjust the starting time (please contact the event coordinator at least 48 hours in advance with details).

  12. Access to the internet or textbook or hard copy of a Periodic table or a similar source is allowed. The rules below lists the recommended website.

  13. Puzzles will be graded in sequential order. For example, if a group submits 8 completed puzzles but # 5 has an error(s), they get credit for puzzles #1-4, assuming they are correct. Also, if a group submits puzzle #'s 1,2,3,8,9 (all correct) only puzzles #'s 1,2,3 will count.

  14. All puzzles should be solved by students without any outside help (teachers, parents, etc) and without any type of electronic puzzle solver.

  15. Only a single word document with 1 completed puzzle and its corresponding table per page will be accepted. There should be a cover page with group names, location, members, and number of puzzles completed. (i.e. 8 completed puzzles = 8 pages)

Form

Your group has to fill out the information/form below, and select the appropriate e-mail address (by group; middle, high school, etc) listed above in the drop down menu of the form.

This has to be completed at least 24 hours in advance (you should receive a confirmation e-mail shortly after submitting this information).

Group Name:
(you choose, i.e. State University Hydrogen atoms)
Group Division:
Group Institution:
Group Address:
Group e-mail address (primary):
(where the puzzle will be sent on the day of the competition)
Group e-mail address (secondary):
Group members names:
Academic Advisor:
Is this group associated with a specific class/course?:
 Yes No
Name/number of course?:
Details:
Recipient:
Security Code:
 

Abstract

A chemistry based puzzle derived from the logic of Latin Squares is described in this paper. Students complete a nine by nine grid in a systematic fashion using a total of 81 different elemental symbols. There are horizontal, vertical, sub-unit (3x3) and alphabetical constraints placed on completing the grid properly. The elements are broken into nine groups based on chemical properties and position on the periodic table. In order to solve the puzzle in an efficient matter a logic pattern is recommended. A number of variations are possible from the original puzzle presented in this paper.

Introduction.

In this paper a chemical riddle derived from the popular numerical game Sudoku ispresented.  The logic exercise outlined here, which has similar numerical constraints as the Suduko but an added level of difficulty due to chemical properties, is dubbed Periodic Puzzles.   In addition to a logic exercise, these puzzles force students to closely examine the periodic table as well as search for and develop pattern recognition schemes.

Numerical logic puzzles developed that are similar to Sudoku include Fillomino, Nonograms, Hotaru Beam, Bag, Kuromasu, and Stained Glass.  These are distributed by the Japanese publisher Puzzle Communication Nikoli, which achieved world-wide fame with their Sudoku puzzle series.1  Sudoku puzzles are based on Latin square logic in which a X×X sized grid filled with X different numbers or symbols. Each number or symbol can appear once in each row and once in each column.  Figure 1 provides a simple example of a simple 3x3 Latin square with 3 symbols (A,B,C).

A B C
C A B
B C A

Figure 1. An example of a Latin Square.

Our group recently developed a logic based algorithm entitled Electronic Qualitative Analysis Schemes (EQAS).2 This is a spreadsheet based approach that teaches students periodic trends by providing a series of clues. Students not only solve EQAS’s but also write their own scheme as part of the exercise. In addition to teaching important chemical concepts, it allowed students to work in teams and to compete with other groups internationally electronically.

As opposed to a Latin squares metholdoy in which a 9x9 puzzle has 9 elements or numbers, the 9x9 grid described here as 81 different elements. The second puzzle is more difficult and is based on nine conjoined 3x3 grids. A number of variations of this original presentation are possible.

Discussion:

As opposed to just 9 numbers used in Latin Squares, the periodic Puzzle uses 81 different elemental symbols. Participants have to come up with nine groups of elements, each group has a minimum of nine elements. Table one gives the parameters needed to divide the elements. The periodic table at http://www.ptable.com/ is the reference point. For the artificial elements, it may be assumed that their position on the periodic table corresponds to some chemical or physical property. For example, element 118, Uuo, is listed with the inert gases so it is assumed it has similar properties to Xe, Kr and Rn.

The periodic puzzle is outlined in figures 2, 3, and 4 and table 2.

The rules for the Periodic Puzzle format are:

  1. Each 3x3 block contains one element from each of the nine groups listed above. Each completed 9x9 puzzle will have 81 different elemental symbols (3 x 3 x 9).

  2. There can not be two elements from the same group (Table 1. 1-9 above) in the same row or column (vertical, horizontal).

  3. Write just the element symbol in the box (no charge, state, subscripts, etc)

  4. http://www.ptable.com/ This periodic table lists all of the elements that can be used in this grid. If the symbol is clicked on, it provides links to stable oxidation states. Symbols for species with up to 118 protons are possible.

  5. Multiple solutions to puzzles are common and multiple symbols may be possible for a specific box.

  6. Each element can be used only once in the entire 9x9 puzzle. There will be 81 total symbols when the puzzle is completed.

  7. Some elements have the potential to be in different groups (i.e. Cl can be a nonmetal or a gas). Once you use an element in one group it can not be used in another group.

  8. Hydrogen (H), Deuterium (D), and Tritium (T) are isotopes but are treated as separate species for potential use as a gas (T2, D2, H2), a singly charged ion (T+, D+, H+) or a nonmetal (T, D, H).

  9. Some species can be applied to different groups according to oxidation state. For example, sulfur can have oxidation states of -2, 2, +4, +6 in different compounds. Only the stable (bold, on periodic table) charges will apply. For example while sulfur is listed with -2, -1, +1, +2, +3, +4, +5, +6, only the more stable ones, designated in bold letters (-2, 2, 4, 6) would count in completing the puzzle. The charge of zero (0) or the neutral elemental species (i.e. S, Fe, Se) is assumed stable for all elements. On web page www.ptable.com pick the “Orbitals” tab and check the “oxidation.” Each element will have the accepted stable oxidation numbers (i.e. Mn is 2,4,7 and Br is -1, 1,3,5).


    10. Figure 2. This empty 9x9 grid contains nine 3x3 sub-grids. Along with the 9x9 grid rules, access to the on-line periodic table, and the nine elemental groups (table 1), this grid is provided to participants.

    Table 1. The nine groups used in this puzzle.  An element used in one group can not be used in another group.

    1. The element is a gas at 1 atm and 0oC.
    2. The elements have a oxidation state of +1 in a complex, salt or dissolved in water. http://www.ptable.com/
    3. The element is one of the lanthanides (La-Lu).
    4. The element is one of the actinides (Ac-Lr).
    5. The element has a stable oxidation state of +2 (complex, salt, dissolved in water).
    6. The element is a nonmetal or a metalloid (all are on or to the right of the metalloid break).
    7. The element is a soft metal or metalloid (left of the metalloid break) or a transition metal with a 4d outer orbital (Y-Cd).
    8. The element is a transition metal with an outer 5d orbital (Hf-Hg).
    9. The element is an artificial element with 104 to 118 protons (Rf-Uuo).

    Figure 3. Below is one pattern that allows the distribution of elements by the different groups (A-I) outlined in table 1. A number of reoccurring patterns can be identified within in this grid. Are other patterns possible?


    Figure 4. One combination of 81 symbols that meets all of the rules and follows the logic pattern outlined figure 4.

    Table 2. Elements and their group assignment to each group for the solved puzzle in figure 4. Only element symbols are used in the puzzle (i..e N not N2, or Na not Na+).

    1. Gas at 1 atm and 0oC: F, He, Rn, Ne, Kr, Xe, UUo, N, O
    2. Oxidation state of +1:  Na, K, Li, Rb, Fr, D, Cs, Ag, T
    3. Lanthanides (La-Lu): Ce, Ho, Nd, La, Yb, Eu, Lu, Gd, Dy
    4. Actinide (Ac-Lr): U, Lr, Fm, Ac, Md, Am, Pu, Np, Th
    5. Oxidation state of +2: Fe, Cr, Be, Zn, Mg, Ba, Ca, Ra, V
    6. Nonmetal or a metalloid: Br, As, S, Si, P, C, B, Se, I
    7. Soft metal, 4d or metalloid:  In, Bi, Po, Al, Sn, Pb, Tl, Ge, Zr
    8. Transition metal (Hf-Hg):  Hf, Ta, W, Re, Pt, Au, Ir, Os, Hg
    9. Artificial element (104 -118): Sg, Uuh, Rf, Uus, Mt, Db, Bh, Hs, Ds


  10. Students are typically asked to consider the pattern they will follow to complete a puzzle (fig. 4) and to designate what elements they are using in each group (table 2). The pattern and elements used (table 2) may change with different puzzles.

  11. Participants are required to submit both a completed puzzle (typed, Word) and a table directly below that that designates which elements were used for each group. Each group in the table should have the nine elements used in the puzzle only. The same group numbering (1-9) used in table 1 should also be used. The 9x9 puzzle and elemental table should be on one sheet of paper with the group name and the puzzle # (8.5 x 11 paper has all four; puzzle, table, puzzle number (upper right) and group name (upper left)).

The same groups outlined for figure 1 and 2 are used in this puzzle. With a complex riddle such as this, a random approach to correctly filling the grid can result in a long problem solving time frame. After allowing students a period of time to complete the puzzle, a pattern or logic behind properly filling the grid is outlined (fig. 5).

Click to download Sample Sheets

Conclusions.

A riddle that is based on the logic of Latin tables but emphasizes basic is outlined. In addition to stressing periodic trends and elemental symbols, it forces students to see patterns to solve the puzzle. The puzzle presented here can be completed individually or in groups and represents a different paradigm when compared to many of the problems students solve. Like a Sudoku puzzle, it can also be presented as partially filled in (i.e. one pre-designated symbol per 3x3 grid).

References

  1. The company list their numerous puzzle publications at: http://www.nikoli.co.jp/en/

  2. TJ. Manning, AP Gramatges, S Ullah, P Vu, L Lasseter, V Kumar,  J Felton, CJ Mock†and G. Fernándezthe Chemical Educator, Vol 13(2), (2008) pp 87-91

  3. Thomas J. Manning: Periodic Puzzles:The Periodic Table, Element Symbols and Pattern Recognition Chem. Educator 14 (2009) 4, 155-157

Click to download Puzzle References