Logic
While walking through a fictional forest, you encounter three trolls guarding a bridge. Each is either a knight, who always tells the truth, or a knave, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave. Each troll makes a single statement:
Troll 1: If I am a knave, then there are exactly two knights here.
Troll 2: Troll 1 is lying.
Troll 3: Either we are all knaves or at least one of us is a knight.
Which troll is which?
troll 1= knight
troll 2= knave
troll 3= knight
The most popular mathematician in the world is throwing a party for all of his friends. As a way to kick things off, they decide that everyone should shake hands. Assuming all 10 people at the party each shake hands with every other person (but not themselves, obviously) exactly once, how many handshakes take place?
45
A={3,4,…,15}. Find | {3,4,…,15}|.
| {3,4,…,15}| = 13
How many committees of 5 students can be selected from a class of 25?
53,130
You encounter three characters in a mysterious town: Alice, Bob, and Carol. Each of them is either a truth-teller, who always tells the truth, or a liar, who always lies. You need to figure out who is who based on their statements.
alice= truth-teller
Bob= liar
Carol= liar
At the warm-up event for Oscar’s All Star Hot Dog Eating Contest, Al ate one hot dog. Bob then showed him up by eating three hot dogs. Not to be outdone, Carl ate five. This continued with each contestant eating two more hot dogs than the previous contestant. How many hot dogs did Zeno (the 26th and final contestant) eat? How many hot dogs were eaten all together?
Zeno= 51
Total= 676
B={n∈ ℕ :2<n≤200}. Find |B|
|B| = 198
A box contains 12 black and 8 green marbles. How many ways can 3 black and 2 green marbles be chosen?
248
You meet three characters: Ethan, Fiona, and George. Each one is either a truth-teller, who always tells the truth, or a liar, who always lies. You need to determine who is who based on their statements:
Who is the truth-teller and who are the liars?
George= truth-teller
Fiona= liar
George= liar
After excavating for weeks, you finally arrive at the burial chamber. The room is empty except for two large chests. On each is carved a message (strangely in English):
This chest is filled with treasure or the other chest contains deadly scorpions
If this chest is empty, then the other chest’s message is true.
.You know exactly one of these messages is true. What should you do?
Choose chest 2
Find two sets A and B for which |A|=5, |B|=6, and |A∪B|=9. What is |A∩B|?
|A∩B|= 2
Three hardcover books and 5 paperbacks are placed on a shelf. How many ways can the books be arranged if all the hardcover books must be together and all the paperbacks must be together?
1440
You meet three people: Alice, Bob, and Carla. Each one is either a truth-teller (always tells the truth) or a liar (always lies). You need to figure out who is who based on the following statements:
Alice= liar
Bob= liar
Carla= liar
Back in the days of yore, five small towns decided they wanted to build roads directly connecting each pair of towns. While the towns had plenty of money to build roads as long and as winding as they wished, it was very important that the roads not intersect with each other (as stop signs had not yet been invented). Also, tunnels and bridges were not allowed. Is it possible for each of these towns to build a road to each of the four other towns without creating any intersections?
no it is not possible
Find sets A and B with |A|=|B| such that |A∪B|=7 and |A∩B|=3. What is |A|?
|A|= 5
How many ways can you pair up 8 boys and 8 girls?
64