With esProc, we could program the game more conveniently. Working out a solution with four random numbers becomes easier:

Let's
analyzes the piece of code in detail.

Four numbers for computation are given in A1. First, we try all possible permutations of the four random cards. To do this, we list the repeatable cases in A2 with the help of a four-digit base-4 number. In B2, we only select those cases which are not repeated. See figure below:

Any three symbols of four arithmetic operations need to be inserted in computation. Each symbol is selected arbitrarily among plus, minus, times and division. Execute in A3 the loop of a three-digit base-4 number, and list all possible combinations:

Different computation orders have different computed results. The computing order can be changed by adding brackets. Three operational symbols show that the computation can be divided into three steps, and brackets adding decides the execution order of the three steps. Combinations in B3, selected from the results in A3,contain all three elements 1,2,3, and represent all possible execution orders. See figure below:

Since there could be repeated numbers among the four randomly selected cards, all permutations of cards will be listed in A4 and remove those repeated ones in B4 in order to avoid redundant loop. Let's look at [8,3,8,3] in A1, its eligible combinations are as follow:

For each
permutation, the programming in line 5 and line 6 executes loop of every symbol
selection and every computation order. Then computes by calling subprogram in
A8 and with the copied parameters to avoid interfering the subsequent
computation.

When the
subprogram in A8 is called, numerical sequence, symbol sequence, and sequence
of computation order should be filled respectively into A8, B8 and C8; at the
same time, expression for computation should be prepared in D8. B9 executes the
loop of sequence of computation order until the result is gradually obtained.
C9 gets the result of a single step by calling subprogram in A13. The
subprogram, which is quite simple, achieves computed results of four arithmetic
operations based on two given numbers and one of the symbols. D9 aims at the
expression used for single step computing, after which the original two numbers
will become one, and expression sequence, symbol sequence and numerical
sequence will be modified in E9, C10 and D10. Having done the single step
computing, the original total computing steps will be reduced by one, so another
modification of sequence of computation order will be required in E10. In line
11, unless it is the last step, brackets will be added to newly-created
expression to ensure an appropriate computing order.

When the
loop in B9 is over, subprogram in A8 completes its computation of expression
for this case. B18 is programmed to decide whether the result is 24. The result
will be calculated to three decimal places in consideration of computational
error of double-precision number. If the result equals to 24, the current
permutation is eligible. The corresponding expression will be put in B1 in C12.

If the
loop of all conditions is finished, yet no expression is found in B1 when
checking A7, no solution has been obtained.

After all
the computation, result can be found in B1. See below:Or cellset parameter will take the place of combination of numerical value entered in A1:

Set cellset parameter before doing computation:

The result displayed in B1 after computation is as follow:

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