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by Michelle Youngs
This month's Puzzle Corner activity is a simplified version of a game
called Fences from the February 2001 Games magazine. The original
version has a 10 x 10 dot grid with the digits 0, 1, 2, and 3 spread repeatedly
throughout. Each digit represents the number of line segments that will surround
that square in a valid solution. For example, a square that contains a 3 would
have line segments on three sides, and a square that contains a 2 would have
line segments on two sides, and so on as shown below.
The challenge is to create a "fence" around the digits by connecting
the points horizontally and vertically, such that each digit is bordered by
the correct number of line segments.
To make the game appropriate for students, the grids in our version are five
by five. Additionally, several of them have more than one solution, which always
increases the chances that students will experience success. A sample grid is
shown below with three different solutions, each of which is corrected based
on the numbers given.
There are three student sheets provided for this activity. The first
challenges students to solve each of the four puzzles in the manner described
above. The second student sheet provides a place for
students to record multiple solutions for the same problem. Encourage students
to search for and record as many different solutions as they can for each problem
(one of the problems has only one solution). The third
student sheet is an option extension for those students who finish quickly
or are looking for an extra challenge. It provides six blank grids in which
students can create their own problems. These problems may be created either
by first drawing a fence and then putting in a few numbers, or by first putting
in a few numbers and then trying to find a fence to fit those numbers. Once
a workable problem is created, students should write the numbers in pen and
trade it with a classmate to solve.
Be sure students use pencils when working on this activity so that they can
erase their incorrect attempts and try again. Another option is to laminate
the first student sheet and have students use dry erase markers to search for
solutions.
There are many possible extensions to this problem in addition to the one given
on the third student sheet. For older students, expand the grid to six by six
or seven by seven to create more difficult problems. Challenge students to create
a problem with more than four possible solutions or only possible one solution.
Determine the fewest number of digits that must be placed in the grid to result
in a problem that has only one solution.
Student Sheet 1 | Student Sheet
2 | Student Sheet 3
I hope that you and your students enjoy this puzzle! Puzzle Corner
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