Multiple choice general knowledge math & puzzles

"I visited my math teacher last February. My teacher told me there were 3 groups of students came to his house on that day already. He also told me each group had different numbers of students. He said it was a coincidence that the product of the numbers of students in each group was equal to the visiting date (today’s date). He asked me if I knew how many people came in each group I looked at the calendar and found out that there might be 4 possible answers. So I asked my teacher a question. He replied: No. Then I gave him the correct answer. How many people came in each group? ‘Do you consider 1 person as a group?’ My teacher said: No. Do you know on what date I visited my teacher?"

  1. 1,2 and 3

  2. 2, 3, and 4

  3. 3,4 and 5

  4. 4, 5 and 6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To solve this question, the user needs to understand the relationship between the number of students in each group, their product, and the visiting date. The user must also consider the possible visiting dates based on the given information.

Let's consider each option and eliminate those that are impossible based on the information provided:

Option A: 1, 2, and 3. The product of these numbers is 6. However, there are no dates in February that are the 6th of the month, so this option is not possible.

Option B: 2, 3, and 4. The product of these numbers is 24. February 4th is the only possible date in February that has a product of 24, so this option is possible.

Option C: 3, 4, and 5. The product of these numbers is 60. However, there are no dates in February that are the 60th of the month, so this option is not possible.

Option D: 4, 5, and 6. The product of these numbers is 120. However, there are no dates in February that are the 120th of the month, so this option is not possible.

Therefore, the only possible answer is:

The Answer is: B. 2, 3, and 4.

AI explanation

This is a classic logic puzzle solved by finding all ways to factor the day-of-month into three distinct group sizes (excluding 1-person groups), where the teacher's "no" to knowing the answer immediately implies there were multiple possible triples for that date, and the follow-up question narrows it to one date with a unique resolvable triple. Working through the February date constraints (max day 28/29) and eliminating dates with a unique factorization until only one date yields exactly the described ambiguity, the group sizes 2, 3, and 4 (product 24, date the 24th) satisfy all the puzzle's stated conditions. Other triples like 1-2-3 are excluded by the "not a 1-person group" rule, and the higher triples don't fit the described ambiguity pattern as cleanly.

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