The Firing Squad Synchronization Problem (FSSP), one of the most well-known problems related to cellular automata, was originally proposed by Myhill in 1957 and became famous through the work of Moore [1]. The first solution to this problem was given by Minsky and McCarthy [2] and a minimal time solution was given by Goto [3]. A significant amount of research has also dealt with variants of this problem. In this paper, from a theoretical interest, we will extend this problem to number patterns on a seven-segment display. Some of these problems can be generalized as the FSSP for some special trees called segment trees. The FSSP for segment trees can be reduced to a FSSP for a one-dimensional array divided evenly by joint cells that we call segment array. We will give algorithms to solve the FSSPs for this segment array and other number patterns, respectively. Moreover, we will clarify the minimal time to solve these problems and show that there exists no such solution.

This paper describes an approach to extending the learning experience using a Web-CAI system incorporated with MATHEMATICA, which is an advanced calculating software widely used in science and engineering fields. This approach provides the possibility of extending access to the courses that students have learned at school. We can use variables in mathematical formulas so that different problems can be shown to students. At the same time, we can also use algebraic formulas. In addition, applying MATHEMATICA to the given process for the answer automatically makes the answer of the problem. And two types of the answer expressions are acceptable which are filling in text by keyboard and selecting by click. This paper presents the design for the system and its specific implementation, and the technical solving scheme. At the end of this paper, the learning evaluations and the problem-editing interface design are discussed.