Mr. Singsong distributed out 4 bags to Allan, Brian, Charlie and David. He said: Each of you have a bag of red and/or white balls. Every bag has 3 balls. The numbers of red balls in all bags are different. Even each bag has a label to indicate what each bag contains, all labels are completely wrong. Now, you can take out 2 balls out from the bag and then tell me what is the color of the third ball.Allan took out 2 red balls from his bag. After he compared the label he told Mr. Singsong what the color of the third ball was immediately.Brian took out 1 red ball and 1 white ball from his bag. After he compared the label he told Mr. Singsong what the color of the third ball was immediately also. Charlie took out 2 white balls from his bag. After he compared the label, he could not tell what color of the third ball was. However, David said to Mr. Singsong: I can tell what color of all my 3 balls are. He did it correctly. But how?
Also, can you tell what label said and what kind of balls each person had?
Mary has a bag of salt which weights 140 grams. She has only 2 measuring chips, one is 7 grams and the other is 2 grams. She wants to separate the bag of salt into 2 bags, one which has 55 grams and the other which has 85 grams. How can you help Mary out using the balance scale to measure just 3 times? It is not necessary to use the chips every time.
Mrs. Harrison has 6 lovely hats, 3 blue, 2 yellow and one pink. Alice, Betty, Cindy and Debbie are lined up as shown in the figure. Mrs. Harrison help them put the hats on hem so they will not see what color hat they have on. Alice can see what color of hats Betty, Cindy and Debbie are wearing. Betty can see what color of hats Cindy and Debbie are wearing. Cindy can see what color hat Debbie is wearing. Debbie can not see any of the hat colors. Mrs. Harrison asks them what color of the hat they are wearing. Alice said she can not tell. Betty said she can not tell either. Cindy also can not tell. However, Debbie was able to tell what color she was wearing after knowing that everyone else could not tell. How did Debbie figure out what color she was wearing?
The figure shown has 13 units of small squares. Cut the figure into 4 pieces, each of the same size and shape, that will fit together and form a perfect square.
We paint each face of the 4 feet cube with the color red, then cut the cube into 64 one foot small cubes.
How many small cubes will have no red color on any side of the cube?
How many small cubes have 1 face with red color? How many small cubes have 3 faces with red color?
