Logic

Uncategorized

Problem Simplification

  1. Screwy pirates
    • 5 pirates 100 coins, voting
  2. Tiger and sheep
    • 100 tigers, 1 sheep
    • tiger eats sheep and becomes a sheep

Others:

Logic Reasoning

  1. River crossing
    • A, B, C, D: 1min, 2min, 5min, 10min
    • 1 torch, 2 people cross at a time
    • minimum total time
  2. Birthday problem
    • Mar 4, Mar 5, Mar 8, Jun 4, Jun 7, Sep 1, Sep 5, Dec 1, Dec 2, Dec 8
    • A knows month, B knows day
    • A says he doesn’t know and C doesn’t know
    • B says now I know
    • A says now I know
  3. Card game
    • 2 cards at a time, both black go to dealer, both red go to player, or discarded, win 100 only if player has more cards
  4. Burning ropes
    • 2 ropes, 1 hour each, burn non-uniformly, measure 45 min
  5. Defective balls
    • 12 balls, 1 defective, 3 times weighing
    • up to $(3^n-3)/2$ balls using $n$ weighing
  6. Trailing zeros
    • trailing zeros of $100!$
  7. Horse race
    • 25 horses, 5 tracks, 5 horses each
    • find best 3, and best 5
  8. Infinite sequence
    • $x$ to the power of $x$ to the power of … is 2, what is $x$

Thinking Out of the Box

  1. Box packing
    • pack 53 1x1x4 bricks into 6x6x6 box
  2. Calendar cubes
    • place single digits on 2 dices to display 01 to 31
  3. Door to offer
    • two doors is offered, one with a car, one with a goat
    • one guard tell lies and other always tells the truth
  4. Message delivery
    • unsecure channel message delivery with two locks
  5. Last ball
    • 20 blue and 14 red balls. Randomly take two balls out each time
    • same color put 1 blue in, different color put 1 red in
    • what is the last ball in the box
    • 20 blue and 13 instead?
  6. Light Switches
    • 1 light bulb and 4 switches in a room, at most 1 time to enter the room
  7. Quant salary
    • Eight quants average

Application of Symmetry

  1. Coin piles
    • 1000 coins on the floor, 980 coin tails, 20 coin heads. separate into two piles to have equal heads
  2. Mislabeled bags
    • 3 bags, 1 bag has 3 white balls, 1 bag has 3 black balls, 1 bag has 1 white and 1 black
  3. Wise men
    • 50 wise man randomly called, putting a glass, to test if anyone can state that everyone has been called.

Series summation

  1. Clock pieces
  2. Missing integers in 1 to 100
  3. Counterfeit coins I
    • 10 bags with 100 coins, 1 counterfeit bag with lighter or heavier 1 gram coins. weight once using digical scale
  4. Glass balls
    • minimum number of glass balls to test the highest floor of a 100 floor building without breaking the balls

The Piegon Hole Principle

  1. Matching socks
  2. Handshakes
  3. Have we met before?
  4. Ants on a square
    • 51 ants on a 1x1 square, find a position so a 1/7 radius circule encompasses at least 3 ants
  5. Counterfeit coins II
    • 10 bags with 100 coins, each bag contains either 9/10/11 gram coins, determine all bags’ type using digital scale in one weighing

Modular Arithmetic

  1. Prisoner problem
    • 100 prisoners, red and blue hat, best strategy to free at least 99
    • what if k colors
  2. Division by 9
  3. Chameleon colors
    • 13 red 15 green 17 blue, two diff colors met -> becomes the third color, will all become the same color

Math Induction

  1. Coin split problem
    • split 1000 coins into 2 piles and obtain xy score, further split until all are in single piles. the final sum will always be the same
  2. Chocolate bar problem
    • minimum breaks to break 6x8 choco into 48 pieces
  3. Race track

Proof by Contradiction

  1. Irrational number
  2. Rainbow hats (hard)
    • 7 color 7 prisoners, guess without communication, at least one correct then all free

Not yet catgorized