General Solution

Let us make the some inferences first, then we will build the table and work from there.

Number of cookies or biscuits received by each student is a natural number from 1 to 9 with each number appearing at least once. – Each number from 1 to 9 appears once, with one number appearing twice.

T receives 8 more cookies than biscuits – T receives 9 cookies and 1 biscuit The person who is last in the queue received 10 items in all, while P receives only half as many totally – P receives only 5 items totally. Either 1 + 4 or 2 + 3 in some order. Number of cookies Q receives is equal to the number of biscuits P receives – This is the number that appears twice. So, the number that appears twice is either 1, 2, 3 or 4. R who was in the middle of the line => R is third.

The total number of cookies is two more than the total number of biscuits distributed. => This is a very vital clue. This tells us that the total number of cookies and biscuits are both odd or both even. Importantly, the total number of cookies + total number of biscuits is an even number.

1+ 2 + 3 + … 9 = 45. So, if the total is an even number, the number that repeats should be odd. We know that the number that appears twice has to be 1, 2, 3 or 4. So, we can further narrow this to 1 or 3. Further, we know that T receives 9 cookies and 1 biscuit. So, the number that repeats is 3. So, number of cookies Q gets = number of biscuits P receives = 3. Number of cookies P receives should be 2.

The overall total number is 48. Total number of cookies = 25, total number of biscuits = 23. Let us consolidate the data we have.

The person first in the queue receives the least number of cookies. Or, P should be first in the queue. R is third. Q is before S in the queue.

Q receives one more good than S and one less than R. T receives 10 and P receives 5. So, Q, R and S together should receive 48 – 15 = 33. Q receives one more good than S and one less than R. Or, Q should receive 11, R should receive 12 and S should receive 10. Either S or T should be last in the queue.

Q is before S in the queue. Or Q is not last. Person second in the queue receives an odd number of biscuits and an odd number of cookies. Q receives 3 cookies and 8 biscuits, so Q is not second. So, Q has to be 4th, Q is before S, so S is last. T is second.

The numbers missing are 4, 5, 6 and 7. R should have received 5 and 7. S should have received 4 and 6. Since the total numbers should also match, we can arrive at two possibilities overall.

Solution to Question 2
Q received 3 cookies. Correct Answer: 3