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?

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.

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?