Pick A Card, Any Card!

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-sized and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either, and you may get a shoutout in next week’s column. If you need a hint, or if you have a favorite puzzle collecting dust in your attic, find me on Twitter.

Riddler Express

From Mike Strong, a climate change problem:

In each of the last three years — 2014, 2015 and 2016 — a new global temperature record has been set. Assuming that accurate temperature records exist since 1880, what is the probability of this happening at random?

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Riddler Classic

From Mont Chris Hubbard, a prediction puzzle inspired by his habit of trying to identify the funniest name as early as possible in a movie’s scrolling end credits:

From a shuffled deck of 100 cards that are numbered 1 to 100, you are dealt 10 cards face down. You turn the cards over one by one. After each card, you must decide whether to end the game. If you end the game on the highest card in the hand you were dealt, you win; otherwise, you lose.

What is the strategy that optimizes your chances of winning? How does the strategy change as the sizes of the deck and the hand are changed?

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Solution to last week’s Riddler Express

Congratulations to 👏 Bob Rietz 👏 of Asheville, North Carolina, winner of last week’s Express puzzle!

In standard American bingo, a bingo card is a five-by-five grid of squares. The columns are labeled B, I, N, G and O, in that order. The five squares in the B column can be filled with the numbers 1 through 15, those in the I column with the numbers 16 through 30, those in the N column 31 through 45, and so on. The square in the very center of the grid is a “free space” on every card. How many different possible bingo cards are there?

There are 552,446,474,061,128,648,601,600,000.

For the four columns B, I, G and O — those without the free space — there are 15 ways to choose the first number in the column, then 14 ways to choose the second, 13 to choose the third, 12 to choose the fourth and 11 to choose the fifth. (The number of options descend because once a number is selected for one square, it can’t appear in another.) For the N column — with the free space in the middle — we need to pick only four numbers: There are 15 ways to choose the first, 14 ways to choose the second, 13 to choose the third and 12 to choose the fourth. Now, we multiply all those possibilities together!

((15cdot 14cdot 13cdot 12cdot 11)^4cdot (15cdot 14cdot 13cdot 12)approx 5.52cdot 10^{26})

 

Solution to last week’s Riddler Classic

Congratulations to 👏 Andrew Zwicky 👏 of Cedar Falls, Iowa, winner of last week’s Classic puzzle!

Imagine that it’s the beginning of time, and the Supreme Court’s…

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