Simulating Multiple Layer Loop to Solve Logical Problems
Please write a program to solve the following 10 questions:
1. Which question is the first question with answer ‘b’?
(a) 2; (b) 3; (c) 4; (d) 5; (e) 6
2. The only two consecutive questions with identical answers are:
(a) 2, 3; (b) 3, 4; (c) 4, 5; (d) 5, 6; (e) 6, 7
3. Which question has the same answer as this one?
(a) 1; (b) 2; (c) 4; (d) 7; (e) 6
4. The number of questions with the answer ‘a’ is:
(a) 0; (b) 1; (c) 2; (d) 3; (e) 4
5. Which question has the same answer as this one?
(a) 10; (b) 9; (c) 8; (d) 7; (e) 6
6. The number of questions with answer ‘a’ is the same as the number of questions with which answer?
(a) b; (b) c; (c) d; (d) e; (e) None of the above
7. How many letters are there between the answer to this question and the next in the alphabet?
(a) 4; (b) 3; (c) 2; (d) 1; (e) 0 (Note: ‘a’ and ‘b’ are one letter apart).
8. The number of questions answered with a vowel letter is:
(a) 2; (b) 3; (c) 4; (d) 5; (e) 6 (Note: ‘a’ and ‘e’ are vowel letters).
9. The number of questions answered with a consonant letter is:
(a) a prime number; (b) a factorial number; (c) a square number; (d) a cube number; (e) a multiple of 5
10. The answer to this question is:
(a) a; (b) b; (c) c; (d) d; (e) e
In these questions, the answers to each question may influence each other, requiring comprehensive judgment. To facilitate incrementing the answers within a loop, the options a, b, c, d and e are represented as 1, 2, 3, 4 and 5 respectively. The program operates as follows: First, initialize all question answers to 0. Then, increment each question’s answer by 1 sequentially, and validate each answer according to the requirements of the corresponding question. If an answer fails to meet the requirements, increment it by 1 until it satisfies the requirements. If all 5 options have been tried without finding a valid answer, backtrack to reset the previous question’s answer. If a question’s answer is 0, skip it without any validation.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | =[0]*10 | >i=1 | ||
| 2 | for i>0 | >A1(i)=A1(i)+1 | ||
| 3 | if A1(i)==6 | >A1(i)=0,i=i-1 | next | |
| 4 | if !func(A8) | next | ||
| 5 | >i=i+1 | |||
| 6 | if i==11 | =C6 | A1.(char(asc("a")+~-1)).concat() | |
| 7 | =C6 | |||
| 8 | func | =A1(A1(1)+1) | if B8!=0 && B8!=2 || A1(to(A1(1))).pos(2)>0 | return false |
| 9 | if A1(2)!=0 | =A1(2)+1 | ||
| 10 | if A1(C9)*A1(C9+1)>0 && A1(C9)!=A1(C9+1) | return false | ||
| 11 | if A1.pselect(~>0 && |
return false | ||
| 12 | if A1(3)!=0 | =A1([1,2,4,7,6](A1(3))) | ||
| 13 | if C12!=0 && C12!=A1(3) | return false | ||
| 14 | =A1.count(~==0) | =A1.count(~==1) | ||
| 15 | if A1(4)!=0 | =C14-A1(4)+1 | ||
| 16 | if C15>0 || C15<0 && B14==0 | return false | ||
| 17 | if A1(5)!=0 | =A1([10,9,8,7,6](A1(5))) | ||
| 18 | if C17!=0 && C17!=A1(5) | return false | ||
| 19 | if B14==0 | =A1.align@a([2,3,4,5]).(~.len()) | ||
| 20 | if !((A1(6)!=5 && C19(A1(6))==C14)|| (A1(6)==5 && C19.pos(C14)== null)) | return false | ||
| 21 | if A1(7)!=0 | if A1(8)!=0 && abs(A1(8)-A1(7))!=5-A1(7) | return false | |
| 22 | if A1(8)!=0 | =C14+A1.count(~==5)-A1(8)-1 | ||
| 23 | if C22>0 || C22<0 && B14==0 | return false | ||
| 24 | if B14==0 | 2,3,5,7],[1,2,6],[0,1,4,9],[0,8],[0,5,10 | ||
| 25 | if C24(A1(9)).pos(A1.count(~>=2 && ~<=4))== null | return false | ||
| 26 | return true |
https://try.esproc.com/splx?38E
A1 initializes all question answers to 0. B1 sets the current question number to i, starting at question 1, and loops through to set the answers.
A2 uses a for loop to traverse each answer of the current question. Within the loop, B2 increments the current question’s answer. B3 checks if the answer is 5; if so, it means all possible answers for the current question have been checked. At this point, the answer is reset to 0, and the program backtracks to the previous question to continue the loop. In each round of the loop, B4 calls the subroutine A8 to check if the current selection conflicts with the question’s requirements. If a conflict is detected, it proceeds to the next answer for the current question. If no issues are found, the program moves to the next question. In A6, determine whether all questions have selected answers that meet the requirements at this point. If true, it indicates that the answer selected in A1 is a feasible solution, which will be recorded in C6. Here, the char and asc functions are used to convert the integer answers to letters, and the concat function is used to concatenate the sequence to an intuitive string.
Let’s now look at the subroutine starting at A8. This subroutine does not use parameters, instead, it directly uses the answers in A1 to perform the check. Also, this subroutine has not been given a name. Therefore, to call this subroutine, you only need to specify its starting cell, as done in B4 with func().
In the subroutine, line 8 checks for mistake based on the corresponding question number in the answer to the first question. First, select the corresponding answer to the question, then check if it is the first ‘b’. If not, it indicates that the current answer to question 1 is incorrect, and the subroutine returns false. If the corresponding answer is 0, it indicates that no selection has been made yet. In this case, the answer to question 1 is not considered incorrect. In SPL, to(n) can generate a sequence from 1 to n, which can be used to retrieve all questions and their corresponding answers selected up to the current point. A.pos(x) is used to check if other questions have selected 2 (corresponding to ‘b’). Logical operators such as OR (||), AND (&&), and NOT (!) can be applied to perform complex conditional checks.
Lines 9-11: Validate the answer to question 2. If question 2 is unanswered, no error is assumed. C10 checks if the answers to the two corresponding questions are the same. Similarly, this check is only performed when both questions have been answered. If the answers are not the same, it returns false. C11 checks if there are any other adjacent answers that are the same. Here, ~[1] represents the answer to the next question. SPL’s syntax allows concise cross-row calculations for such scenarios.
Lines 12-13: Continue to validate the answer to question 3. To do this, first retrieve the answer corresponding to the question number, then determine whether it matches the answer to question 3.
B14 counts the total number of unanswered questions in A1, while C14 counts how many questions have selected ‘a’. SPL uses the count() function to calculate the total number of members that satisfy the conditions.
Lines 15-16: Validate the answer to question 4. This validation can only be performed when all answers in A1 have been confirmed. It verifies whether the total number of questions answered with‘a’matches the condition specified by question 4’s answer.
Lines 17-18: Validate the answer to question 5. It checks if the answer to the corresponding question is identical to the current answer.
Lines 19-20: Validate the answer to question 6, which, like question 4, requires that all answers have been selected. C19 calculates how many times ‘b’, ‘c’, ‘d’, and ‘e’ each appear in the answer. The function align@a(A) groups the sequence according to the order specified in A and then calculates the total number of members in each group. C20 checks if the answer to question 6 is wrong. For the first four options, it verifies if the corresponding answer matches the number of occurrences of ‘a’. If option ‘e’ is selected, it checks if the number of occurrences of ‘a’ is different from all other options.
Line 21: Validate the answer to question 7. It checks if the answers to questions 7 and 8 differ by 1. This check can only be performed when the answer to question 8 has been selected. SPL provides various mathematical functions, including abs() for absolute value calculation, which is consistent with tools like Excel.
Lines 22-23: Validate the answer to question 8. This check can only be done when all answers in A1 have been confirmed. It verifies whether the total number of questions answered with ‘a’ and ‘e’ matches the answer.
The answer to question 9 is complex. The checking process involves several steps. First, select prime numbers, factorials, squares, cubes, and multiples of 5 from the possible total number of questions (0-10). Then, in C25, verify whether the number of questions with answers ‘b’, ‘c’, or ‘d’ matches the answer to question 9.
Actually, any option is valid for question 10, as it only affects the validation of the preceding questions. If the answers to the first nine questions are all correct, then the current solution is deemed valid.
The problem has 5 answer options for each question, which essentially equates to 10-layer nested loops. By setting up the answer array in A1, a single-layer loop simulates the equivalent operations of multi-layer loop. By immediately validating whether answers are invalid after each question’s selection, unnecessary loops are also avoided. If multiple nested loops were to be executed, it would require 5^10 calculations, which is extremely computationally intensive, resulting in significantly worse performance than this method. After execution, only one set of answers satisfies the requirements:
