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  • Imagine that a family has two children, one of whom we know to be a boy. What then is the probability that the other child is a boy? The obvious answer is to say that the probability is 1/2—after all, the other child can only be either a boy or a girl, and the chances of a baby being born a boy or a girl are (essentially) equal. In a two-child family, however, there are actually four possible combinations of children: two boys (MM), two girls (FF), an older boy and a younger girl (MF), and an older girl and a younger boy (FM). We already know that one of the children is a boy, meaning we can eliminate the combination FF, but that leaves us with three equally possible combinations of children in which at least one is a boy—namely MM, MF, and FM. This means that the probability that the other child is a boy—MM—must be 1/3, not 1/2.

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  • prisionor-warden-puzzle

    23 selected prisoners are summoned by the warden. He gives them a choice of playing a game with him that might ensure their escape from the prison or might as well lead them towards painful death. The prisoners think that this is the only chance for them to be free again and agrees to him.

    The warden tell them that there is a room which has just two switches which are labelled 1 or 2. The switches may be up or down and the condition is not known at present. They are not connected to anything. The warden may select any prisoner on any day and send him to the switch room. The prisoner will have to select any one switch and reverse its position i.e. if it is up, he will turn it down and if it is down, he will turn it up. He can and must only flip one switch and then he will be confined to his cell again.

    The warden may choose the same prisoner more than one time and he will be choosing completely randomly. But at a certain point of time, everyone will have visited the switch room. And at any time, the prisoners may declare that everyone has visited the room at least once. If they will be true, they will be set free but if they will be wrong, they will be killed.

    The warden gives them an hour to plan any kind of strategy and then they will be confined to their respective cells and will never be allowed to meet. What strategy can help them be free?

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  • The Scoop
    Tristan’s sister Angela and her four friends love to share their most recent diary entries with each other at sleepovers. This last sleepover, Tristan was able to snag each of the girls’ diaries after they fell asleep. He flipped through them and found that each girl had a different crush, a different favorite shade of nail polish, and a different preference in ice cream flavors – and each of them had a big, juicy secret! See if you can figure out what he learned about each of his sister’s friends – and his sister.

    The Choices
    Girls: Angela, Mandy, Savannah, Alyssa, and Lily
    Crushes: Josh, Noah, Luke, Ben, and Sam
    Nail Polish Shades: Lavender, Lime, Banana, Sky, and Crimson
    Ice Cream Flavors: Rocky Road, Rainbow Sherbet, Cookie Dough, Reese’s Peanut Butter, and Raspberry Cheesecake
    Juicy Secrets: Still sleeps with a blankie, Loves lima beans, Hates Justin Bieber, Is really into cars, and Wants to be a lunch lady

    The Clues
    Tristan read five different entries for January 7th. One said, “Noah said, ‘Nice hair, Savannah,’ and I felt special.” Another said, “My nails are purple again, just like I like them.” A third said, “I wish Luke would look at me.” The fourth said, “I lost my beloved blankie this morning.” The last said, “I’m dying for some more of that rainbow sherbet.”

    “January 8th. Dear Diary, I accidentally chipped one of my perfect, lime-green nails today while doing my daily private anti-Justin Bieber ritual.”

    “January 9th. Dear Diary, Josh caught me examining his awesome antique Chevrolet after school today. I guess I was kind of hoping he would.”

    “January 10th. Dear Diary, Angela was writing a love note today. I tried glancing over her shoulder, but all I caught was the second letter of its recipient’s name, which looked like either a U or an A, and something about being a lunch lady before she yanked it away.”

    “January 11th. Dear Diary, I hope Sam likes the color red…I also hope he doesn’t mind girls who still sleep with blankies…”

    “January 12th. Dear Diary, I think it’s funny that both me and Savannah like nail polishes that are named after fruits. Love, Alyssa.”

    “January 13th. Dear Diary, I saw Sam eating Reese’s Peanut Butter ice cream yesterday. Could this be a sign that we’re meant to be? Love, Mandy.”

    “January 14th. Dear Diary, I just noticed that the name of my favorite shade of nail polish has something majorly in common with my name, and Alyssa’s favorite shade starts with the same letter as her crush’s name.”

    “January 15th. Dear Diary, The girls were over at my house last night, and someone flicked cookie dough ice cream at me. It couldn’t have been Angela, who will only eat raspberry cheesecake ice cream, and Savannah was in the bathroom…”

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  • There was a death on Treebark Ln. The victim was identified as Mark Oswalt, who recently was married. The police went to the crime scene and they reported the death as a suicide.

    Later that day, after the police left, a private detective, hired by the victim’s friend who thought it was a murder, searched the crime scene and found a note the police missed.

    It read,

    “4,3: 8,1:_: 9,1: 2,1: 7,4:_: 6,1:9,3:_: 9,1: 4,3: 3,3: 3,2: !”

    The detective took out his cell phone and started dialing the police to tell them about his findings. Once the detective opened the phone to dial, he immediately screamed out, “I SOLVED IT!”

    Who was the murderer and how did the detective find out?

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  • To enlist the help of the other kingdoms, the king talked to the queen about inviting neighboring royalty to dinner. This put the queen into a royal snit. Theirs was not a very wealthy kingdom and the royal dinnerware was in a disgraceful condition. Apart from ordinary dishes for everyday use, all that the royal pantry contained were a few dinner plates of three different
    dinner patterns:
    1. five silver ones with birds
    2. six crystal with seashells
    3. seven gold with the royal crest
    They were all stored in disarray on a very dark top shelf of the royal pantry. Only those would be suitable for entertaining other royalty.
    If the queen didn’t want to climb up to the top shelf twice, how many dinner plates would she have to take down to be sure she had matching dinner plates for herself, her royal spouse, and for the neighbouring king and queen?

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  • Kim Jones, Jan Robinson and Pat Smith are the officers
    of the spaceship. They serve as the craft’s pilot,
    engineer and biochemist, though not necessarily in that
    order. Because they have difficulty with Martian names,
    they nickname the three Martians who work with them
    Jones, Smith and Robinson.
    1. Robinson is a Yomi.
    2. Jones doesn’t speak any language other than
    3. Most Martian linguists are Uti.
    4. The Martian who serves as interpreter respects the
    Martian whose name is the same as the biochemist’s.
    5. The Martian whose name is the same as the biochemist
    is a Grundi.
    6. Jan Robinson beat the engineer at chess.
    Who is the pilot?

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  • Martians don’t need to develop airplanes as a means
    of moving through the air. Most feathered Martians can
    fly easily. Every few lunars, feathered Martians from
    the various groups participate in a tournament to determine
    which are the best fliers of the planet.
    This lunar, teams of two feathered Martians from
    three groups are competing:
    1. One team is from the Uti, one from the Grundi,
    and one from the Yomi.
    2. Each team is made up of one female and one male.
    3. The female participants are Xera, Wora, and Teta.
    4. The males are called Vel, Pyi, and Rir.
    5. Despite her daring feats in the air, Teta had never
    been away from home before the contest.
    6. Xera and Rir had never met before the tournament.
    7. Xera will be visiting Pyi’s group when the Yomi go
    on a special excursion to that part of the planet.
    8. Pyi admires Teta’s colorful feathers, as well as her
    ability to soar, and once watched her and her teammate
    in the territory of the Grundi.
    If the winners are members of the Uti group, what
    are the names of the best fliers?

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