Kentertainment Boxes

A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship? What was in each carton?

Kentertainment, Term 1 Week 8 (from KenKen.com)

There is a three digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number? You must prove your answer, please!

Kentertainment, Term 1, Week 7 (from KenKen.com)

A, B and C all told each other about the age and gender of X. All three of them told at least one truth. A: X is male and age 20 B: X is male and age 22 C: X is female and age 18 What is the age and gender of X?

Kentertainment, Term 1, Week 7 (from KenKen.com)

A ship anchored in a port has a ladder, which hangs over the side of the boat. The length of the ladder is 200cm, the distance between each rung is 20 cm and the bottom rung touches the water. The tide rises at a rate of 10cm per hour. When will the water reach the fifth rung?

Kentertainment Term 1, Week 6 (from KenKen.com)

A weighs half as much as B, and C weighs three times as much as A. Together, they weigh 720 kilograms. How much does each letter weigh?

Looping 2

For this looping trick you start with any two numbers from 0 to 9 and follow this rule: add the two numbers and write down just the digit that is in the ones place. 

For example, start with 8 and 9. Adding them gives you 17. Keep just the 7, which is in the ones place. Now you have 8-9-7. Add the last two numbers, the 9 and the 7. That gives 16; just keep the 6, then you have 8-9-7-6. Keep going, adding the last two numbers in the series each time, keeping only the digit in the ones place. Do this until you get 8 and 9 again. Then the loop starts all over. How many numbers are in the 8-9 loop before it repeats? 

What happens with 2 and 6?

Does the order of the numbers you choose make a difference?

Post your ideas and findings! Remember to write your name at the beginning of your post. 

Looping 1

Start with any number you like and follow these rules. If the number you start with is even, divide it in half. If the number is odd, multiply it by 3, then add 1. Whatever answer you get, apply one of these rules to it again. Do it over and over again - that's the looping part. 

For example, start with 10. It's even, so take half. That gives you 5. That's odd, so multiply it by 3 and add 1: (5x3) +1 = 16. Back to even, so take half and get 8. Half again gives you 1. Since 1 is odd, multiply it by 3 and add 1 to get 4. Half of 4 gives you 2, and half of that gets you back to 1. You're in a loop now and will be forever if you keep at it. 

Try the same procedure with 30 and see what happens. 

Try a few more. What do you notice? Does something happen each time? Write a post to explain what you discovered. Remember to begin each post with your name. 

Poison

Poison is a game for two people. For the first game, use thirteen objects. Players take turns removing one or two objects. Play until all objects have been taken. The last object to be removed is considered to be the poison. Whoever gets stuck taking it loses. What is your winning strategy?

King Arthur's Problem

King Arthur's daughter wanted to marry. She loved maths and created a problem for King Arthur's knights to solve. The knight who solved the problem would prove himself to be logical and brave, therefore worthy to become the lucky husband. The knights were told of the problem in advance and could choose whether or not to compete for the daughter's hand, but they were not told that King Arthur would not actually chop off anyone's head. All of the knights were to gather and be seated at the round table, then King Arthur would point to the knight in the first chair and tell him, "You live." To the next, rather unlucky knight, King Arthur would point and say, "You die." To the third knight he would say, "You live," and to the fourth, "Off with your head!" He would continue doing this around the table, chopping off the head of every other knight, until only one knight remained alive. The remaining knight would marry King Arthur's daughter. Where is the safe seat? Find the safe place to sit with different numbers of knights. Find a pattern so you can predict where to sit no matter how many people are seated in the circle. You need a strategy and method for recording your findings such as, when there are 12 knights, the safe seat is ___; when there are 20 knights, the safe seat is ___. Think about your strategy, then talk to a friend before you begin. You may work with a partner if you wish. Be sure to put both names at the beginning of your post when you share your discoveries.

Great Games: Pico Fermi Bagel

Pico Fermi Bagel is a guessing game for two players, or two teams, and uses quite a bit of strategy. Each player thinks of a number (use three digit numbers to begin with) and you take turns guessing the other person's number. Whoever guesses the other person's number first wins. With each player's guess, the other player must give clues. Use the clues in order to make a strategic next guess. There are three clues:

Pico means that one of the guessed digits is correct but is in the wrong place;

Fermi means that one of the guessed digits is correct and is also in the correct place;

Bagel means that none of the digits in the guess are correct.

Think Time: Abacus Beads

 

This diagram shows a simple abacus with nine beads representing the number 324.

a. If there are twenty beads and all must be used, what is the largest number that can be represented?

b. What is the smallest number that can be represented?

c. If there are almost the same number of beads on each column, what numbers can be represented?