Problems for Breakthrough Thinking
- Creative writing
(Each 20 pts)
1.Write a short story based on the drawings given to you in class.
2. Write a story, given the first sentence “Once upon a time there was a hen that had forgotten how to lay eggs”
- Combinatorial problems
1. Name 20 different ways to use a brick. Determine as many properties of a brick as you can. For each usage name the property that made the usage possible.
(5 pts)
2. Name 12 different ways to use a pencil. Determine as many properties of a pencil as you can. For each usage name the property that made the usage possible.
(5 pts)
3. Word ladders : Change just one letter at each step to go from the left word to the right word. Do not change the order of the letters. Example: cart – cast – cost – coat – goat
(Each 5 pts)
3.1. calf – bull
3.2. moon – beam
3.3. hard – soft
3.4. fool – wise
3.5. work – rest
3.6. foot – ball
3.7. side – walk
3.8. left – hand
3.9. snow – fort
4. Choose a word among the words given below and construct at least 100 shorter words using only the letters in the source word. Within a constructed word, a letter may be used as many times as it appears in the source word.
Words with 2 letters or less and personal names are not allowed.
For example, if the source word is constellation, you can construct “nation”, “nations”, but you cannot construct “constants” because “s” appears only once in “constellation”
(each 10 pts)
Sample source words
constellation
industrialization
penetratingly
notwithstanding
warehouseman
hereinafter
kindhearted
diplomatically
fundamentally
thereabouts
emancipation
extraordinary
international
5. Insert appropriately the signs + , -, *, /, and parentheses between the numbers to find the total. You are not required to use all signs and to use parentheses.
(Each 5 pts)
5.1. 1 2 3 4 5 6 7 8 9 10 = 33
5.2. 1 2 3 4 5 6 7 8 9 10 = 62
5.3. 1 2 3 4 5 6 7 8 9 10 = 80
5.4. 1 2 3 4 5 6 7 8 9 10 = 30
5.5. 1 2 3 4 5 6 7 8 9 10 = 50
6. Alphametics (Category B – combinatorial)
Assign digits to letters (different letters correspond to different digits, same letters to same digits) so that the arithmetic operations are correctly done
6.1 to 6.6 each is worth 5 points
6.7is worth 10 points
6.8
6.1
VOLVO
+ FIAT
------
MOTOR
6.2
TEMPO
+TEMPO
TEMPO
------
HECTIC
6.3 6.4
MIXALORS
+ FUNALORS
AND + NOUS
------NOUS
MATH ------
LAVONS
6.56.6
LOAN CAT
+LOAN + DOG
LOAN ------
------PETS
DEBT
6.7
AAB + CBC = DDEA
+ - +
FDF - ADF = GEE
HFD + KFG = DAEA
7. There are four people who want to cross a bridge; they all begin on the same side. You have 17 minutes to get them all across to the other side. It is night, and they have one flashlight. A maximum of two people can cross the bridge at one time. Any party that crosses, either one or two people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown, for example. Each person walks at a different speed: person 1 – 1 minute to cross the bridge, person 2 – 2 minutes, person 3 – 5 minutes, person 4 – 10 minutes. A pair must walk together at the rate of the slower person’s pace. For example, if person 1 and person 4 walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If person 4 returns the flashlight, a total of 20 minutes have passed and you have failed the mission. How can you get all four persons across the bridge for 17 minutes?
(10 pts)
- Logical Problems
The solution of the problems below has to contain your reasoning. i.e. you have to describe how you have reached your conclusions. Each problem is worth 10 points
1. Four friends have been identified as suspects for an unauthorized access into a computer system.
They have made statements to the investigating authorities.
Alice said: "Carlos did it"
John said: "I did not do it"
Carlos said: " Diana did it"
Diana said: " Carlos lied when he said that I did it"
- If the authorities also know that exactly one of the four suspects is telling the truth, who did it?
- If the authorities also know that exactly one is lying, who did it?
2. Five friends have access to a chat room. Is it possible to determine who is chatting if the following information is known:
- Either Kevin or Heather or both are chatting.
- Either Randy or Paul but not both are chatting.
- If Abby is chatting, so is Randy
- Paul and Kevin are either both chatting, or neither is.
- If Heather is chatting than so are Abby and Kevin.
3. Somebody marked the six faces of a die with the numbers 1, 2 and 3 - each number twice. The die was put on a table. Four people - Abu, Babu, Calu and Dabu - sat around the table so that each one was able to see only three sides of the die at a glance
Abu sees the number 1 and two even numbers.
Babu and Calu can see three different numbers each.
Dabu sees number 2 twice and he can't remember the third number.
What number is face down on the table?
4. A famous violinist was in town for a concert. While he was away from his room for a short time his favorite violin, a Stradivarius, was stolen. Inspector Detweiler took immediate action, and through diligent research was able to identify four suspects. Each of them makes one statement as follows. The guilty one’s statement is false; the other statements are true.
A. I was not in town at the time of the theft
B. C is the culprit
C. B’s statement is false
D. C’s statement is true
Which one is guilty?
5. A professional burglar has recently managed to actively pursue his criminal activities by targeting the homes of the most affluent villagers. The inspector is on the trail of the culprit and has identified four suspects, one of whom is missing. The other three are questioned.; each makes two true statements and one false statement.
A. 1. I am not the burglar
2. D has no alibi.
3. D went into hiding.
B.1. A’s first statement is true
2. A’s third statement is false
3. D is not the burglar
C.1. I am not the burglar
2. D has no alibi.
3. B’s second statement is false
Can the inspector identify the burglar?