Saturday, March 25, 2017

10-digit Number

Find a 10-digit number where the first digit is how many 0's there are in the number, the second digit is how many 1's in the number, the third digit is how many 2's, and so on, until the tenth digit which is how many 9's there are in the number.

Click below to see the answer.

Saturday, March 18, 2017

The Extra Dollar

Here is an old math puzzle that you can find many versions of online.

Two friends have a meal at a restaurant, and the bill is $25. The friends pay $15 each, which the waiter gives to the cashier. The cashier gives back $5 to the waiter. The friends tell the waiter to keeps $3 as a tip, so he hands back $1 to each of the two diners.

So, the friends paid $14 each for the meal, for a total of $28. The waiter kept $3, and that makes $31. Where did the extra dollar come from? Give yourself a moment to think about it before clicking below for the solution.

Saturday, March 11, 2017

Arranging Eights

Can you arrange eight 8's so that when added they will equal 1000? Click below to see the answer.

Saturday, March 4, 2017

A Unique Number

What is unique about the number 8,549,176,320? Click below to see the answer (and a bonus question).

Saturday, February 25, 2017

Best Poker Hand

Which of the following poker hands is the best? Assume one standard 52-card deck is used. The game is five-card draw, so there are no community cards, with no wild cards.

For reference, here are the rankings of poker hands.
  • Royal flush - A, K, Q, J, 10, all the same suit.
  • Straight flush - Five cards in a sequence, all the same suit.
  • Four of a kind - Four cards all of the same rank.
  • Full house - Three of a kind with a side pair.
  • Flush - Any five cards, all the same suit
  • Straight - Five cards in a sequence, any suits.
  • Three of a kind - Three cards all of the same rank.
  • Two pair - Two different pairs.
  • One pair - Two cards of the same rank.
  • High card - Highest card in your hand.

Click below to see the answer.

Saturday, February 18, 2017

The Collapsing Bridge

The bridge will collapse in 17 minutes! Four people need to cross the bridge before it collapses. It is a dark night and they have only one flashlight among them.

Only two people can cross at a time.
  • Alice takes one minute to cross.
  • Bob takes two minutes.
  • Carol takes five minutes
  • Dave takes 10 minutes to cross.
How can they all get across before the bridge collapses? Click below to see the answer.

Friday, February 10, 2017

The Island of Knights and Knaves

Raymond Smullyan, one of the grand masters of logic puzzles, sadly passed away at the age of 97 earlier this week. In his honor, I present a classic puzzle adapted from his book What Is the Name of This Book?

There is a wide variety of puzzles about an island in which certain inhabitants called "knights" always tell the truth and others called "knaves" always lie. It is assumed that every inhabitant of the island is either a knight or a knave.

In this problem, there are only two people, A and B, each of whom is either a knight or a knave. A makes the following statement: "At least one of us is a knave." What are A and B?

Click below for the solution.

Raymond Smullyan presented a couple more of his puzzles in a 1982 interview on the Tonight Show with Johnny Carson. When you see the white hair and long beard, it seems like even 35 years ago that Smullyan was an old man, but the twinkle in his eye and the playfulness in his voice reveal that he was always a child at heart. Watch the full interview below.

If these puzzles seem too easy, they're just a small sample of Dr. Smullyan's brilliant work. If you really want a challenge, I encourage you to check out some of his books, or The Hardest Logic Puzzle Ever, also credited to Smullyan.

Finally, I leave you with a quote.

Why should I be worried about dying?
It's not going to happen in my lifetime!

-Raymond Smullyan (1919 - 2017)