Part A:Questions1–6
Each question should be answered by a single choice from A to E.
Questions are worth3points each.
1.DNA quence
Molly is processing long DNA quences such as the following:
A A A T C C C C C A A G A A A A A
She encodes this quence as A3T1C5A2G1A5,a saving of five characters. How many characters are saved if she encodes the following quence?
T T T T T G G G A C C C C C C G A A
(A)6(B)7(C)8(D)9(E)10
2.Artworks
Jermaine creates most wonderful artworks!She paints in a very particular style. She starts with a9by9grid of squares,all white except for the one in the middle; it is black.
Then,she picks any white square that shares a side with one and only one other black square and colours it black,repeating this until she is happy.
You attend an art show hoping to buy one of Jermaine’s works.But there are lots of imitations and fakes on display!Which one is Jermaine’s?
A B C D E
(A)A(B)B(C)C(D)D(E)E
3.Bookshelf
Terri is moving veral numbered books from her bookshelf to her desk.She takes a book from either end of her bookshelf,but always puts it at the left on the desk.For instance,if she had books 213on her bookshelf,and took the leftmost book
(2)from the bookshelf,then the rightmost book (3),then the remaining book (1),they would be in order 132on her desk.黑皮病症状图片
Bookshelf
Desk
Move book 2Move book 3Move book 1Terri has 7books on her bookshelf,in the order 2364715.
She notices that the books form a number.She decides to make that number as large as possible,still following her ‘take from either end,place on left end’rule.What is the number on the fifth book from the left after she has moved all 7books?
(A)1(B)2(C)3(D)4(E)5
4.Taking Half
Amy and Bob are playing a game.They start with a large pile of pebbles and take turns to remove one or more pebbles.On a player’s turn:
•If there is only one pebble left,the player removes that pebble.
•If there is more than one pebble left,the player can remove up to half of the pebbles remaining.
The winner is the player who removes the last pebble.
茉莉花的养殖方法There are 24pebbles and Amy plays first.How many pebbles should she take on her first turn to ensure that she can win the game,assuming she plays optimally throughout?
(A)1(B)3(C)7(D)10(E)12
爱党5.Flow Diagram
Flow diagrams provide a visual way of showing a process or algorithm:a box is ud for an action,a diamond(shaded)for making a decision,and arrows indicate the flow of control.
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Each of the values23,47,119,and123456in turn is input to the flow diagram below.
How many of the outputs are even?
(A)0(B)1(C)2(D)3(E)4
6.Triangular Walk
A robot can only walk horizontally to the left,up right at60°from the horizontal,or down right at60°from the horizontal.
←←←
The robot goes on the walk shown below.
←←←←←←←←←
←←←←←←
←←←←←←←←How many more instructions are needed for the robot to return to its starting position?
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(A)4(B)5(C)6(D)7(E)8
Part B:Questions7–9
Each question has three parts,each of which is worth2points.
Each part should be answered by a number in the range0–999.
7.Maximum Plus–Minus Sum
A sublist of a list of numbers is a t of one or more adjacent elements from the list.
For example,546and4641are both sublists of the list546412.(There are many other sublists.)
The plus–minus sum of a sublist is obtained by alternately adding and subtracting the numbers in the sublist.
For example,the plus–minus sum of546is+5−4+6=7,whilst that of464 1is+4−6+4−1=1.
In each of the following lists of numbers,find the sublist with the largest plus–minus sum.Your answer will be this sum.
A.46823472
B.42687437
C.8647615682475
8.Tweet Spots
Two or more robots are walking from left to right along parate tracks.The tracks are made up of squares and each square of the track is either a plain or a tweet spot square.
During each cond:
十二生肖兔•If a robot is on a plain square,it will take a step to the right.
•If a robot is on a tweet spot square,it will not move,unless all robots are on a tweet spot square.It will then tweet to the other robots(which takes no time)and then will take a step to the right.
On the tracks below,the tweet spot is shaded,and each robot is reprented by an R.
R
R
Start After2cs After4cs After5cs After7cs The robots will tweet after4conds,and both robots will be on the last square after7conds.
港琪月饼For each of the tracks below,how many conds will it take for all robots to reach the last square?(7in the example above.)
A.
B.
C.
9.Evolving Numbers
A number with an even number of digits can evolve into a new number by extract-ing pairs of adjacent digits and placing them at the start of a new number. Consider the number451972.It could evolve into429751as shown in the table below.
Extract51514972
Extract97975142
Extract42429751–
By choosing different pairs of adjacent digits along the way,the original number could have evolved into veral different numbers.
Your task is to find the largest possible evolved number.
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For each of the following strings of digits,what are the last three digits in the largest number that can be evolved from the string?
A.37594156
B.52730819
C.9453678152
