Using Matlab for Solving Differential Equations [jnl

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Extra resources for Using Matlab for Solving Differential Equations [jnl article]

Example text

This relation also holds for a combination of sequences, where the numbers h, m, b, i, and s refer to the combination, as can be seen by adding the relations for the separate sequences. The relation can be rewritten as follows: 2(h - b) + (m - i) = 2s - 9(2h + m). If I is the number oflow digits, and 0 that of the ordinary digits of the combination, then h + m + I = b + i + 0, because both members are equal to the number of digits of the combination. So one also has 2s - 9(2h + m) = 2(h-b) + (m - i) = (h - b) + (0 -I) = (i - m) + 2(0 - I).

9 20. Nwnber of solutions of the crossing puzzle. We consider the simplified crossing puzzle of§19 (with 10 squares, 2 white and 2 black pieces), and assume, as before, that the white pieces move straight across. According to Figure 9, 15 sequences of the moves 1,2,3,4, b, C are possible. Each of these sequences provides a certain number of places at which move a can be performed and a certain number of places at which move d can be performed. As the order of moves a and d is immaterial, you should multiply the 2 numbers to get the number of possibilities pertaining to the order of moves a and d relative to the assumed order of the other moves.

The engine first pulls A to the right of Q, and next takes A to the turntable. Now L moves to the right, past Q, then to the left past P, and then to the left-hand side of the turntable. The engine L then takes A to the left, past P, and next moves back, with A, until it is between P and Q. The same thing can be done even with car B present. B is first taken to the right (past Q) sufficiently far that it is not in the way when A is being shunted. When A has been taken to the right of L, the same operation is performed with car B.

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