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.