Senior Challenge 2
Question 1
 When
Class 7R filed into their classroom on the day before the Easter break,
they could see they were in for a surprize.
Their teacher, Mr Benny Rabbett, had placed seven plates
at each table and there were mini-Easter eggs on each plate.
“Let me explain before you start fighting about which
place to choose!” said Mr Rabbett.
“When I say “Go”, everyone gives half their Easter eggs to the
person on their right. If someone has an odd number of eggs, they behave
generously and give their neighbour that extra half egg. For example, the
person with 3 eggs will pass on 2 rather than 1 ½ eggs. When everyone at
a table has the same number of eggs, then you may consume them. But first,
you must find out how many times I will be saying “Go”.
The Naturally Mathematical team soon had their answer,
and thought that everyone was being made to wait too long before tucking
into the eggs, so they asked:
“Mr Rabbett, please can we re-arrange the plates so that you don’t
have to say “Go” so often.”
What was the answer to Mr Rabbett’s question that the
team found, and what was the re-arrangement of plates that they suggested?
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Question 2
The Naturally Mathematical team had completed their
solution to Q1 and were about to enjoy their hard-won Easter eggs.
“Not so fast!” said Mr Benny Rabbett. He had started
his computer and wanted to show them a logic puzzle that was baffling
him.
“Before you start on those Easter eggs, I need you to
solve this puzzle. It goes like this. You have to remove all the squares.
When you click on a green square, it is removed … watch me.” and Mr
Rabbett showed the team how clicking on a green square removes it and he
also showed them that clicking on a red square did nothing.
“However, “ said the teacher, “any square next to
the green one you click on changes colour, red to green or green to red.
You can change the number of squares, so that you can try the puzzle with
between 1 and 20 squares. But, please do not touch those Easter Eggs until
you have discovered a strategy for winning the puzzle … if it can be won
at all.”
Both Mr Rabbett and his team of naturally mathematical
students need some help with this one.
They would like to know:
- A good strategy for winning the puzzle.
- A rule for deciding if a particular puzzle can be
won.
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Question 3
 “Now,
team, I am sure that you will not be happy until you have won this Prize
Easter Egg.” said Mr Benny Rabbett to his Naturally Mathematical team.
“To win the egg, enter the numbers 1 – 16 into these
squares to make the four numbers in the each of the diagonals add to the
same diagonal total. At the same time, the four numbers in the red
squares and the four numbers in the yellow squares should add to the same square
total, which can be different to the diagonal total.”
“But there are some rules. No two consecutive numbers
can be in squares that are next to each other – either horizontally
or vertically or diagonally!”
Before handing over the Prize Easter Egg, Mr Rabbett
would like to know:
- What is the smallest diagonal total than can be made?
- What is the largest diagonal total that can be made?
- How can the diagonal and square totals be made the
same?
At least he has provided an applet to help you show him
that the Prize Easter Egg should be yours!
To start the applet, click on the diagram of squares,
and use it add numbers to the grid. In your answer, please include only
one example for each of the three questions, as there are lots of ways in
which each one can be achieved. |
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