A safe has a code lock that unlocks if you input the correct four digits, in any order. The lock has a keypad the the digits 0, 1, 2, ..., 9. For example, suppose the unlock code is 1000. The safe will open for any order you input the digits: 1000, 0100, 0010, 0001. How many different unlock codes are there? (Two unlock codes are different if they do not contain exactly the same digits.) Watch the video for two different methods to solve this puzzle.

My blog post for this video:
https://wp.me/p6aMk-5cG

Tim Morris emailed me a wonderful write-up connecting the two methods and the Chu-Vandermonde identity. Do check it out! It's beautifully formatted and very nicely explained. Here is the link to the pdf on Google Drive: https://drive.google.com/file/....d/0B8VTzkx-EaCAU0xGN

TOUGH Interview Question - Ways To Give 11 Coins To 3 People
https://youtu.be/HdBX-Hn2uYo

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My Books

"The Joy of Game Theory" shows how you can use math to out-think your competition. (rated 3.9/5 stars on 29 reviews) https://www.amazon.com/gp/product/1500497444

"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 5/5 stars on 2 reviews) https://www.amazon.com/gp/product/1523231467/

"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. https://www.amazon.com/gp/product/1517421624/

"Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1517531624/

"Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews) https://www.amazon.com/gp/product/1517596351/

"40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) https://www.amazon.com/gp/product/1517319307/

"The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) https://www.amazon.com/gp/product/150779651X/

"Multiply Numbers By Drawing Lines" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 3 reviews) https://www.amazon.com/gp/product/1500866148/