Lenore is a sweepstakes hobbyist. She identifies profitable contests and sends in multiple entries. She benefits from the fact that sweepstakes sponsored by commercial products cannot require those who want to enter the draw to buy a product. If they did, the customer would be paying to enter so the contest is really a lottery. It would then be subject to laws that govern gambling.

But sweepstakes are different. While you would typically be offered a chance to win a McDonald’s sweepstake when you buy a Big Mac, the entry form will specify in small print how to submit entries without buying anything. Lenore is one of many sweepstakes enthusiasts who spend hours submitting entries without buying anything. When the entry form is mailed, the only cost to Lenore is her time, stationery, and postage.

Another requirement of lotteries is that the number and types of prizes be fixed. This is in contrast to types of gambling where a contest offers a chance, albeit small, of being won over and over with no end in sight.

Here’s how a typical old-school sweepstake works. The entries are placed into boxes. Once one box is full, another is started. Each box can contain a different number of entries. When it’s time for the draw, a box is chosen at random and a winning entry is picked from that box.

Now the question: To increase the odds of winning a sweepstake, one self-help book for sweepstakes gamers suggests to Lenore that she spread her submissions over the duration of the contest.  Then she will not have “all her eggs in one basket.”  Rather, she will have her submissions spread over a large number of boxes. Thus, when a box is picked at random, there is a better chance that her submission will be in the box, which gives her a better chance of winning. At the other extreme, if all of Lenore’s entries are in a single box and that box is not chosen, then her chances of winning are zero. Thus, spreading her submissions over a number of days increases her chances of winning. 

Is this advice is right, wrong, or somewhere in between? Check in next Monday to see if you got it right.

Solution to Micro Softy 27: Diamond in the Rough  

In last week’s Micro Softy, Keith wanted to propose to his beloved Priscilla with a $15,000 diamond ring from his jeweler brother Nevil. Because Keith couldn’t afford that, Nevil suggested he buy a $500 cubic zirconium ring instead. Sensing Keith’s disappointment at this, Nevil proposed a deal: The diamond ring would be mixed with 250 fakes in a bag. For $600, Priscilla would be allowed to pick one ring — real or not. Keith, a probability theorist, then negotiated for the rings to be split into two bags, allowing Priscilla to choose a bag and then a ring. Nevil agreed and allowed Keith to arrange the contents of the bags as he wished.

Clever Keith then put the single diamond ring in one bag and all the fakes in the other. Priscilla now had a 50‒50 chance of choosing the diamond ring.

You’ll be glad —and perhaps not altogether surprised—to know that Priscilla got the diamond.

Links to all the Monday Micro Softies

Monday Micro Softy 27: Diamond in the rough Why did the mathematician want all the diamond rings — hundreds of fake ones, plus a real one — divided into two bags? The solution to Micro Softy 26 lies in recognizing that there are different ways of measuring distance.

Monday Micro Softy 26: Arguing with Pythagoras. Will the diagonal of a triangle with sides of 3 and 4 feet be 5 feet or, as a visiting mathematician suggests, 7 feet? The answer to last week’s puzzle lies in remembering what happens when you put a rod on a diagonal inside a square box.

Monday Micro Softy 25: The Fishing Rod Blues The Memphis bus driver was sympathetic but he couldn’t let Johnny ride with his overlong fishing pole. Johnny solved the problem—but how?
About last week’s Micro Softy: You CAN have a tie in 3D Tic Tac Toe. We illustrate it. And we show what the 4D game is like.

Image Credit: fotomolka - Adobe Stock

Monday Micro Softy 24: Have you ever tried 3D Tic Tac Toe? To liven up a predictable game, try doing it in three — or even four — dimensions! You won’t be bored. To solve the Barnum’s Circus ticket receipts puzzle, recall that X, Y and Z must all be whole numbers. Algebra then enables us to work out the solution.

Monday Micro Softy 23: Barnum’s Circus Receipts. Circus master Barnum’s ticket seller had not kept proper track of the tickets sold. Can the limited information — and some algebra — help Barnum figure it out? The solution to Micro Softy 22, given here, depends on the assumptions we make about Timmy’s surgeon.

and

Monday Micro Softy 22: Can there be two daddies? This week’s puzzler asks: Can a child’s father be dead and alive at the same time? Or is there another solution? The solution to last week’s puzzler lies in things we can do with binary numbers.

Monday Micro Softy 21 and previous links: Finding More of the Deadly Fentanyl Pills. There, you will also find links to Microsofties 11 through 20 as well.

At Monday Micro Softy 11: What Happened to That Other Dollar?, you will find links to the first ten Micro Softies. Have fun!