Các bài toán logic trong đề thi APMOPS 2004


Question 1:

A box of chocolate has gone missing from the refrigator. The suspects have been reduced to 4 childrens. Only one of them telling is the truth.

John      :  “I did not take the chocolate.”

Wendy  :  “John is lying.”

Charles :  “Wendy is lying.”

Sally     :  “Wendy took the chocolate.”

Who took the chocolate?

Hint : Với những bài kiểu này thì ta chỉ cần giả sử từng người một lấy chocolate, từ đó đếm xem có bao nhiêu người nói thật và bao nhiêu người nói dối rồi kết luận kết luận. Hoặc một hướng khác là giả sử từng người là người nói thật, rồi xét các mâu thuẫn và kết luận.

Answer : John.

Question 2:

A particular month has 5 Tuesdays. The first and the last day of the month are not Tuesday. What day is the last day of the month?

Solution:

Notice that there are 29 days from the first Tuesday to the fifth Tuesday. Moreover,  the first and the last day of the month are not Tuesday. Hence, this month has 31 days and we can conclude that the last day of the month is Wednesday.

Question 3:

What is the missing number in the following number sequence?

2,  2,   3,   5,   14,   ?,   965.

Solution:

We can see that a number in the sequence can be obtained by multiplying two last numbers and then minus 1:

2.2-1=3

2.3-1=5

3.5-1=14

5.14-1=69

14.69-1=965

Thus, our answer is 69.



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