Wednesday, 13 August 2014

THURSDAY CHALLENGES

It's not too late to enter the draw for the family prize.  Email me answers to any of the days and you will be entered - once for every question you answer.

Try these last few puzzles.  The draw will take place during assembly and answers will be posted on Monday for you to check your thinking and reasoning against.

EASY
You must cut a birthday cake into exactly eight pieces, but you're only allowed to make three straight cuts, and you can't move pieces of the cake as you cut. How can you do it?

EASY
Can you place six X's on a Tic Tac Toe board without making three-in-a-row in any direction?
MEDIUM



Wednesday Challenges

EASY


You must cut a birthday cake into exactly eight pieces, but you're only allowed to make three straight cuts, and you can't move pieces of the cake as you cut. How can you do it?


HARD

Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).
1. They grow 12 different varieties.
2. Everybody grows exactly 4 different varieties
3. Each variety is at least in one garden.
4. Only one variety is in 4 gardens.
5. Only in one garden are all 3 kinds of crops.
6. Only in one garden are all 4 varieties of one kind of crops.
7. Pear is only in the two border gardens.
8. Paul's garden is in the middle with no lily.
9. Aster grower doesn't grow vegetables.
10. Rose growers don't grow parsley.
11. Nuts grower has also gourd and parsley.
12. In the first garden are apples and cherries.
13. Only in two gardens are cherries.
14. Sam has onions and cherries.
15. Luke grows exactly two kinds of fruit.
16. Tulip is only in two gardens.
17. Apple is in a single garden.
18. Only in one garden next to Zick's is parsley.
19. Sam's garden is not on the border.
20. Hank grows neither vegetables nor asters.
21. Paul has exactly three kinds of vegetable.

Who has which garden and what is grown where?

Tuesday, 12 August 2014


TUESDAY CHALLENGES:

FAMILY FUN CHALLENGE:

Find the solution to this problem all together by getting some checkers pieces out:

 There are four black counters lined up on one side and four white counters lined up on the other side on a 4x4 grid.

The counters can only move diagonally, any number of spaces (just like a bishop in chess).

What is the least number of moves it takes to get all the black counters lined up where the white ones started and the white counters lined up where the black ones started?

Rule: counters cannot jump or land on top of one another.

MEDIUM CHALLENGE:

Felix is a ferryman.  He has a small boat and takes people back and forth across the River Dee.  His charges are:

ADULTS:  $2.50
TEENAGERS:  $1
CHILDREN 50 cents

Some days he has lots of passengers and some days he has just a few.  Last Tuesday morning, Felix noticed something a bit special - he had ferried 20 passengers (some adults, some teenagers and some children) and he had collected exactly 20.

Work out how many of each type of passenger there must have been on Tuesday morning to make this possible.

mathswarriors.co.uk
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HARD CHALLENGE FOR PARENTS AND FAMILIES



A solo dice game is played where, on each turn, a normal pair of dice is rolled. The score is calculated by taking the product, rather than the sum, of the two numbers shown on the dice.
On a particular game, the score for the second roll is five more than the score for the first; the score for the third roll is six less than that of the second; the score for the fourth roll is eleven more than that of the third; and the score for the fifth roll is eight less than that of the fourth. What was the score for each of these five throws?

Saturday, 9 August 2014

MONDAY CHALLENGES:

Easy:
A rope ladder hangs over the side of a ship so that the ladder just reaches the water.  The rungs are 25 cm apart.  How many rungs will be under water when the tide has risen one metre?

Hard: 
A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:
There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?