On the Block

Posted on May 20, 2013 by laura

We aren’t talking about building blocks here, or street blocks: we’re talking about the auction block. Sometimes when lots of grown-ups (or kids) want to buy the same item, the seller can put it up for “auction.” All the interested buyers decide what they’re willing to pay – they “bid” – and the highest bidder wins the item and has to pay that amount. In a live auction, bidders call out higher and higher numbers and the last one standing wins it…so sometimes people get competitive and get stuck paying a lot more than they planned. In a “sealed auction,” you just put your bid in an envelope and all envelopes are opened at once; the high bid wins and that’s it, no second chances. As we’ll see here, there are other ways to run auctions – and maybe to score an awesome deal.

Wee ones: If someone bids $3 for a 1960′s Raggedy Ann doll, and you bid $3 more than that, how much will you have to pay?

Little kids: Live bidding goes up in “increments,” or jumps of a certain size. If an old-fashioned Mickey Mouse coin sorter has a current bid of $25 with increments of $5, how much will the next bid be? Bonus: If the increments after that become $10, what will be the next bid after that?

Big kids: If there’s a sealed auction for the first American Girl doll ever, and the 3 bids are $54, $12 more than that, and then $25 more than the middle bid, what’s the winning bid? Bonus: In a “Dutch auction,” the auctioneer calls out prices that get lower until the first person who’s willing to pay calls out. If bidding starts at $90 with $2 increments for each drop in price, and you have $75 on you, how many prices do you have to skip before you can bid?

Answers:
Wee ones: $6.

Little kids: $30. Bonus: $40.

Big kids: $91, since the middle bid is $66. Bonus: 8 prices to skip. The price has to drop to $74, which is $16 lower, requiring 7 drops in prices that you skip along with the original $90 bid.

Triple Crowns

Posted on May 18, 2013 by laura

Three really is a magic number, and we love it when things happen in threes. It’s very exciting in sports, like when a hockey player scores three goals in one game, which is called a hat trick. An even more exciting threesome is the triplet of major US horse races: the Kentucky Derby, the Preakness Stakes, which happens tonight, and the Belmont Stakes. When the same horse wins all three of those races in the same year, it’s called a Triple Crown. This almost never happens: only 11 horses have ever managed to do it, and the most recent did so in 1978! But every year since Sir Barton won all three in 1919, we wait with bated breath to see if the Derby winner can at least win the Preakness and set the stage for a triple crown…and tonight it’s Orb’s big chance.

Wee ones: If a horse wins the first 2 of the 3 major races, how many races does the horse have left to win to score a Triple Crown?

Little kids: Starting in 2002, 5 horses have won the first 2 races but not the third, including I’ll Have Another last year. How many years from 2002 through 2012 have we not had a double winner? Bonus: From 2002 to 2012, how many major races were run in total?

Big kids: The last horse to get a Triple Crown was Affirmed in 1978. How many years ago was that? Bonus: If 20 horses ran in each race, and each time they all had the same chance of winning, what are the chances of the Derby winner winning the Triple Crown?

Answers:
Wee ones: 1 more race.

Little kids: That span includes 11 seasons, not 10 (this is the “fencepost problem” where you have to count both ends), so there have been 6 years with no double winner. Bonus: 33 races in those 11 years.

Big kids: 35 years. Bonus: 1 in 400. The winner of the first has a 1/20th chance the second time, and then faces those chances again. (Just to clarify, the chances of a specific horse winning all three are 1 in 8000, whereas the chances of any horse winning all three are 1 in 400.)

Give Me a Sign

Posted on May 16, 2013 by laura

Billboards are those big rectangular signs along the side of the highway, usually trying to talk you into buying something. Since they’re a good 50 feet above you, these signs are even bigger than they look – they’re 20, 30, or even over 40 feet wide. The size depends on the speed of the traffic: the faster you’re driving, the easier it has to be for people to read it, so the bigger the letters and pictures need to be. The signs along slower streets in town, called “posters,” are 22 feet wide, but the big “bulletins” along the highway are up to 48 feet wide. Now we have digital billboards that light up like a computer screen and change the picture every few seconds, showing drivers even more things they should buy. Either one works, as long as we read it quickly: the more important thing as a driver is to keep your eyes on the road.

Wee ones: Which one is wider, a 20-foot-wide poster or a 40-foot-wide billboard?

Little kids: If a billboard is 10 feet tall and the bottom is 50 feet off the ground, how many more of those same signs could you stack edge to edge below it? Bonus: If you want to climb up to that 50-foot sign but all you have is an 8-foot ladder, how many more feet does your ladder have to reach?

Big kids: If an adult’s face is 9 inches tall, and all objects on a billboard are 12 times life size, how tall is a face shown on a billboard? Bonus: These giant highway signs are about as big as a house. If the front of a house has a 15-foot-wide kitchen, a 6-foot-wide hallway, and an 18-foot-wide living room, which one is wider, the house or a 48-foot-wide highway billboard?

The sky’s the limit: Suppose as a prank you decide to climb up a billboard at night and wrap a string of lights around the edge. If you need exactly 82 feet of strung lights to cover all four sides, and the area of the billboard (length times width) is 400, what are the width and height of the billboard?

Answers:
Wee ones: The billboard is the bigger number.

Little kids: 5 more of those signs. Bonus: 42 more feet.

Big kids: 108 inches, or 9 feet! Bonus: The billboard would be wider if leaned up against the house – 48 feet vs. 39.

The sky’s the limit: It’s 25 by 16 feet. We know that the width and height have to add to 41, since those two sides will use up half the lights. Those same two numbers also multiply out to 400. You can use trial and error to test the factors of 400 numbers: 40 by 10 doesn’t work, nor does 20 by 20, but 16 by 25 does. Expressing this using algebra:
w + h = 41, so h=41-w
w x h = 400. Replacing h, you get
w x (41-w)=400
41w – w^2=400, or w^2-41w+400=0
…and then you still need trial and error to break it down into
(w-25) x (w-16)=0. So w=16 or 25.

Work Hard, Play Hard

Posted on May 9, 2013 by laura

You can tell from their name what tugboats do: they tug other boats. Tugboats move ships that can’t move themselves, like heavy barges, and steer big ships through crowded areas so they don’t crash into each other. Tugboats can also act as icebreakers, help fight fires, and rescue sinking ships. And to top it off, they can do dance routines: today the annual “Tugboat Ballet” kicks off in Germany, in which eight tugboats swim around to waltz music blasted over loudspeakers, to show off how zippy they are. They also show off their speediness in tugboat races in cities around the world, and the New York race also features a nose-to-nose pushing contest and a line toss competition. Tugboats may not be the biggest boats out there, but it’s clear they have the most fun.

Wee ones (counting on fingers): If 2 of the 8 tugboats scheduled to take part in the Tugboat Ballet break down at the last minute, how many tugboats can still do the show?

Little kids: In the nose-to-nose pushing contest, if one boat pushes the other back 14 feet, but then that boat pushes the first boat 21 feet from there, how far from the starting point do they end up? Bonus: A tugboat can push up to 40 barges, all way bigger than itself! If each barge weighs 5 times as much as the tug, how many times its weight does a tug pulling 20 barges tow?

Big kids: In the New York City tugboat race, the tugs start next to 79th Street in Manhattan and end at a pier next to 44th Street. How many blocks do they travel? Bonus: In last year’s race, the first boat crossed the finish line in 5 minutes and 1 second, and the last one in 12 minutes and 48 seconds. How many total seconds passed between the first boat’s finish and the last?

Answers:
Wee ones: 6 tugboats.

Little kids: 7 feet in front of it. Bonus: 100 times.

Big kids: 35 blocks. Bonus: 467 seconds (7 minutes 47 seconds).

“So Three Ducks Walk into a Hotel…”

Posted on May 7, 2013 by laura

It all started in the 1930′s, when Frank Schutt, the manager of the Peabody Hotel in Memphis, decided to put three live ducks in the fountain in the hotel lobby for fun. Hotel guests thought it was hysterical, so the owners bumped the number up to five ducks. A few years later, a circus animal trainer trained the ducks to walk on their own up to the fountain every morning and back to their pen at night. To this day, the Peabody Ducks march to and from the fountain every day on a royal red carpet, posing for photos along the way. Hopefully they don’t have to carry a suitcase, too.

Wee ones: Apparently the Peabody Hotel fountain had turtles and alligators before the ducks showed up. If the fountain had 8 turtles but now has the 5 ducks, how many more turtles were there than ducks today?

Little kids: The ducks march to the fountain at 11 am every morning and back out at 5 pm every afternoon. How many hours do they spend swimming in the fountain each day? Bonus: How many hours each day do they spend outside the fountain? (Reminder: a day has 24 hours.)

Big kids: These probably aren’t the same 5 ducks from the 1930s. If all Peabody ducks live 8 years and can be trained when they’re 1 year old, what is the earliest year that the current ducks could have started marching? Bonus: If ducks started marching in 1935, what’s the fewest number of sets of ducks the hotel has had to train?

The sky’s the limit: The alligators that used to live in the fountain are long gone, fortunately for the ducks. But ducks would be safe with turtles. If we had 7 more ducks than turtles but 18 more turtle feet than duck feet, and the number of duck feet had the same two digits reversed, how many turtles and ducks would be swimming in the lobby fountain?

Answers:
Wee ones: 3 more turtles than ducks.

Little kids: 6 hours. Bonus: 18 hours.

Big kids: 2006 (7 years ago). Bonus: That was 77 years ago, so they have to have had 11 sets and are on at least their 12th set.

The sky’s the limit: There are 23 ducks and 16 turtles. If the two foot-count numbers are 18 apart and the digits are reversed, then the two digits themselves are 2 apart: so it’s 42, 53, something like that. But they have to be even numbers, so your only choices are 24/42, 46/64, and 68/86. 46/64 gives you animal counts that are 7 apart: 46 duck feet for 23 ducks, and 64 turtle feet for 16 turtles.