487: The Fifteen Puzzle

Everyone older than ten knows that there is a way to play tic-tac-toe so that you can never lose. Any game that can be played to a draw unless someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:


Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.

Is there a guaranteed winning strategy for Player 1?
Is there a guaranteed winning strategy for Player 2?

source:

Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.

— Chris Lusto (@Lustomatical) July 16, 2015

How does his later comment help? "It’s equivalent to tic-tac-toe since any row/col/diagonal in a 3x3 magic square sums to 15, but more mathematically interesting."

486: The Bowling Pins Puzzle

Everyone older than ten knows that there is a way to play tic-tac-toe so that you can never lose. Any game that can be played to a draw unless someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:

There are thirteen pins and the two players take turns bowling.When bowling, you can knock down any pin or two adjacent pins (but not two that are separated by a space) that you like.  The loser knocks over the last pin.

The gnome has bowled first, knocking down #2. How do you best play this game so that you are guaranteed to win?

If you go first, what is your best play?

source: Loyd's Encyclopedia, 1914.

366: Minimal Math Cube

You only get to make one and you've only got 6 sides. What are the six most important items of math in your opinion? What would you put on your Minimal Math Cube?

209: Lewis Carrol's Roses

Nine roses are planted in a circle. If you find that tedious, show how you can rearrange the roses to get:

• Eight rows of three-in-a-row.
• Nine rows of three-in-a-row.
• Ten rows of three-in-a-row.

from Lewis Carroll.

136: Jeopardy!

Assuming that you get every question correct, and bet it all on the Daily Double, and the Daily Double happens at the most opportune time, and the Daily double is located in the absolute best place, how much can you win in the first round of Jeopardy?

And what is the best place for the Daily Double?
And the best time to get the Daily Double?

The prizes are twice as big when you get to the Double Jeopardy Round:

So let's keep this going ... how much can you theoretically win to this point?

In Final Jeopardy, you can bet it all ("Let it Ride", as gamblers say).

123: Binary Names

@MathCurmudgeon @crstn85 Great math question here: how many of these questions would you need to get right before you could ID the teacher?
— Bowen Kerins (@bowenkerins) April 25, 2014

66: Go Fish with Primes

3 William Carey, on a Dan Meyer post:

We play Prime fish with the sixth and seventh graders. You need a special deck of cards, but it’s an easy deck to make (edited, - ed.):

Ten cards with a "2" on them (or two fish)
Ten cards with a "3" on them (or three squid)
Eight cards with a "5" on them (or five eels)
Five cards with a "7" on them (or seven sea-slugs)
Two cards with a "11" on them (or eleven shrimp)

Each player draws four cards. They multiply their hand together, and announce only the product (!) to the group. They then play go-fish.

It’s fun to watch the kids debate whether there’s a strategy to the game. It’s more fun to watch them work out the strategy once they decide that there is a strategy. 

What's the strategy?

24: Arithmetic Challenge

Choose the path through the grid that you feel will gather the most points. You start out at the bottom with 1 point.

While moving from the starting point to the goal, calculate your score by using the "+", "x", and "-" symbols along the way. Calculate at each step - order of operations is turned OFF for this puzzle.

For example: N-N-N-N-N-N-E-E-E-E-N would earn 54 points. Post your maximum in the comments!

You can cross your own path, but you can't take the same route twice, or return along a path you've already taken.

Copyright(c) 2003 Ryosuke Ito

21: Change this 9-Clock to 8s

Or sevens, or sixes, or whatever strikes your fancy.

18: Breaking twenty-five

In this "Tiny Math Games" post by Dan Meyer, there's an idea from [Malcolm Swan]

Pick a number. Say 25. Now break it up into as many pieces as you want. 10, 10, and 5, maybe. Or 2 and 23. Twenty-five ones would work. Now multiply all those pieces together.


What's the biggest product you can make?

What's your strategy?

Will it always work?

Does it work for fractions?

Is there another set of numbers you could use that isn't explicitly against the stated rules?