Draft Lecture 1. Logical reasoning

[yongcheng3315]

Lecture 1. Logical reasoning (posted)

      File (1) Basic knowledge  (444.38 KB - downloaded 200 times.)
      File (2) problems and solutions (337.82 KB - downloaded 198 times.)
      File (3) Exercises and answer keys. (339.802 KB - downloaded 189 times.)

[shanyecunmin]

Thank you ! Very appreciate.

[kellydai]

thank you very much!

[mathcount66]

Thank you so much!!!

[helenwyz]

Thanks a lot, Yongcheng.

[聊天猫]

Lecture 1. Logical reasoning (posted)

      File (1) Basic knowledge  (444.38 KB - downloaded 200 times.)
      File (2) problems and solutions (337.82 KB - downloaded 198 times.)
      File (3) Exercises and answer keys. (339.802 KB - downloaded 189 times.)

More chapters can be found here:

http://www.mymathcounts.com/Forum/index.php?board=43.0

Yongcheng,
I think problem 17 in the file (2) should be like this:
40-5=35
Every time the centipede goes up 5-3=2 feet
36/2=18
total is 18+1=19 days

[yongcheng3315]

You are correct.

I made the correction several days back in the files posted in "50 lectures group" but forget to repost the new file here.

Thanks anyway.

[xyz]

Chapter_1_Logical_reasoning_03  #7,   your answer is 42.

7. The teacher whispers positive integer A to Anna, B to Brett, and C to Chris. The students don’t know one another’s numbers but they do know that the sum of their numbers is 14. Anna says, “I know that Brett and Chris have different numbers” . Then Brett says, “I already knew that all three of our numbers were different” . Finally, Chris announces, “Now I know all three of our numbers”. What is the product ABC?

My son said that 42 is not the only answer, for example:if  A=1, B=2, C=11;
A+B+C=14   product ABC = 22.
if  A=1, B=5, C=8; A+B+C=14   product ABC =40. etc...
So, there are many answers. 
Is my son correct?

[ppw]

Anna says, “I know that Brett and Chris have different numbers” . ==> Anna has an odd number

Then Brett says, “I already knew that all three of our numbers were different” . ==> Brett has odd number 7, 9, or 11. Anna has 1, 3 or 5.  "ALREADY" means Brett did not use Anna's information.

Finally, Chris announces, “Now I know all three of our numbers”. ==> Chris has 6, Brett has 7 and Anna has 1.

===> 1X7X6 = 42

[xyz]

But A can be 3, B can be 7, and C=4,
Then 3*7*4=84
or A=5  B=7  C=2   then 5*7*2=70,    etc....

[ppw]

C can not be 4. If C is 4 then (A, B) could be either (1, 9) or (3, 7). So Chris could not have known all three numbers.

C can not be 2 for the same reason. If C is 2 then (A, B) could be (1, 11), (3, 9), or (5, 7). So Chris could not have known all three numbers either.

If C=6, then the only possible (A, B) is (1, 7). So Chris could tell all three numbers.

Since C must be an even number less than 7, looks like 6 is the only answer.

[jennifer]

Here is my thoughts:
1). From Anna -> Anna is odd
2). From Brett -> Brett is odd, Chris is even, And Brett can only be 7, 9, or 11.
At this point, we still have 6 possibilities: 1+7+6, 3+7+4, 5+7+2, 1+9+4, 3+9+2, 1+11+2. Anna could be 1 or 3,  Brett could be 7,9, or 11, Chris could be 2,4, or 6
3). From Chris -> Since Chris says he knows all 3 numbers, then he must be 6. Because if he is 4, there are 2 possibilities. If he is 2, there are 3 possibilities. Only if he is 6, there is only one possibility which is: Anna must be 1 and Brett must be 7.

[xyz]

When Anna says, “I know that Brett and Chris have different numbers” . Why  Anna must has an odd number? 

Brett can be 4, and  Chris can be 8, then Anna is 2.  Anna can has an even number, still satisfy A, B, C, all different numbers, and A+B+C=14.

[yongcheng3315]

I see you are serious about math problem solving skills. I then really suggest that you register for the 50 Mathcounts lectures. Your child will learn a lot from it.

Good luck!

 

When Anna says, “I know that Brett and Chris have different numbers” . Why  Anna must has an odd number? 

Brett can be 4, and  Chris can be 8, then Anna is 2.  Anna can has an even number, still satisfy A, B, C, all different numbers, and A+B+C=14.

[kevinyizhao]

Why i can not see the draft for download? Do I have to register the class first? Where can I see some sample? Thx.