Three boxes are completely mislabeled, and you need to fix the problem. You can point to a box to get a sample fruit, and you can ask for as many samples as you want. What's the least amount of samples you need to guarantee you can fix the labels?

0:00 problem
1:30 attempt
2:25 solution
5:22 part 2
6:58 lucky
9:00 logic

References
https://www.indeed.com/career-advice/interviewing/puzzle-interview-questions
https://www.glassdoor.com/Interview/There-are-three-boxes-one-contains-only-apples-one-contains-only-oranges-and-one-contains-both-apples-and-oranges-The-b-QTN_114922.htm
https://www.youtube.com/watch?v=KCT_DhnIp9E

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How many can you solve?

0:00 puzzle 1
1:40 puzzle 2
3:14 puzzle 3
4:58 puzzle 4
6:08 puzzle 5
7:34 puzzle 6
9:07 puzzle 7

Puzzle 1
Draw without lifting
https://www.core77.com/posts/77744/Fun-for-Designers-Three-Quick-Can-You-Draw-This-Without-Lifting-Your-Pencil-Tests
Coin
https://commons.wikimedia.org/wiki/File:1884_trade_dollar_rev.jpg
Puzzle 3
https://en.wikipedia.org/wiki/Coin_rotation_paradox
Puzzle 4
https://myworldtheirway.com/2019/10/matchstick-puzzles-changing-directions/
Puzzle 5
https://richardwiseman.wordpress.com/2012/02/13/answer-to-the-friday-puzzle-142/
Puzzle 6
Car parking puzzle
https://www.businessinsider.com/math-question-from-hong-kong-elementary-school-test-2014-6
Puzzle 7
Math Stackexchange
https://math.stackexchange.com/questions/2404176/square-square-square-30-with-boxes-filled-using-1-3-5-7-9-11-13-15
Quora
https://www.quora.com/Mathematical-Puzzles-What-is-+-+-30-using-1-3-5-7-9-11-13-15

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People are saying this problem is impossible, and they are correct.

0:00 problem
1:45 brute force
3:17 proof

Reddit AskMath
https://www.reddit.com/r/askmath/comments/1i5yy92/the_math_book_of_my_cousin_is_scary/

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"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews
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"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews
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"The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
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A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews
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"Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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0:00 intro
0:45 review
2:16 problem 1
5:06 problem 2

Problem 1
https://www.reddit.com/r/askmath/comments/16los83/found_this_scrolling_on_instagram_how_do_i_solve/
Problem 2
https://www.reddit.com/r/askmath/comments/1i6mm0w/found_this_on_ig_you_are_supposed_to_find_the/

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"The Joy of Game Theory" rated 4.2/5 stars on 564 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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Thanks to Daneesha for the suggestion! This question from Sri Lanka's 2021 G.C.E A/L Combined Maths exam paper had an error that the test makers overlooked!

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My Books (worldwide links)
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Mind Your Decisions: Five Book Compilation
https://amzn.to/2pbJ4wR
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"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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What is the smallest number that has exactly 426 proper factors? Special thanks this month to: Lee Redden, Mike Robertson, Daniel Lewis, Kyle. Thanks to all supporters on Patreon and YouTube!
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UCLES STEP Mathematics I, 2009, Q1
https://undergroundmathematics.org/divisibility-and-induction/r7465/solution

9:50 small misspeak, should be "times 3 to the power of 3"

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Book ratings are from January 2023.

My Books (worldwide links)
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Mind Your Decisions: Five Book Compilation
https://amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.3/5 stars on 290 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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Your fingers are secretly a powerful calculator.

0:00 intro
0:23 multiply 6 to 9
7:18 why works 6 to 9
11:52 multiply 11 to 15
15:40 why works 11 to 15
17:14 times table 9
19:28 why works table 9

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http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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Can you solve this? Two circles with radii r and s have common tangents of AB and PQ with lengths AB = 16 and PQ = 14. What is the value of rs, the product of the radii lengths?

rtwodrew2 video, problem at 8:33
https://youtu.be/Q3MUSkIgPhc?si=fc0gWBfFLC1PHiBT&t=514

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http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
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"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
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"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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The original 1926 exam was insanely difficult compared to today's test. This video shares a sampling of questions. ➡️thumbnail question skip to 16:18

0:00 intro
1:24 definitions
4:23 arithmetic
8:07 classification
11:12 artificial language
12:23 antonyms
13:36 number series
16:18 thumbnail question
17:43 analogies
20:14 logical inference
23:07 paragraph reading
25:14 experimental
https://en.wikipedia.org/wiki/SAT
https://satsuite.collegeboard.org/sat/whats-on-the-test/structure
https://www.washingtonpost.com/news/answer-sheet/wp/2014/04/22/heres-the-very-first-sat-from-1926-can-you-pass-it/
https://commons.wikimedia.org/wiki/File:Scholastic_Aptitude_Test_%28SAT%29_from_1926.pdf
https://en.wikisource.org/wiki/Page:Scholastic_Aptitude_Test_(SAT)_from_1926.pdf/1
https://www.erikthered.com/tutor/sat-act-history.html
https://www.erikthered.com/tutor/SAT-1926-Report.pdf
SupertutorTV
https://youtu.be/tKAEaTpgPQ0?si=POF5ZQlBEkcxd5Ym&t=709

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Mind Your Decisions: Five Book Compilation
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"The Joy of Game Theory" rated 4.2/5 stars on 564 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

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https://www.patreon.com/mindyourdecisions

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https://mindyourdecisions.com/blog/press

How many can you solve?

0:00 puzzle 1
3:00 puzzle 2
7:07 puzzle 3

References
https://x.com/AonghasCrowe/status/1843790315314130987
Thanks to Eric from Miami for puzzle 3
Trig verification in puzzle 3
https://drive.google.com/file/d/1Ll1SfK94N9mgqPRzxaNGGyv9u-YTAHVJ/view?usp=sharing

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Book ratings are from January 2025.

My Books (worldwide links)
https://mindyourdecisions.com/blog/my-books/#worldwide

My Books (US links)
Mind Your Decisions: Five Book Compilation
https://amzn.to/2pbJ4wR
A collection of 5 books:
"The Joy of Game Theory" rated 4.2/5 stars on 564 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.2/5 stars on 55 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 81 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 148 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.5/5 stars on 57 reviews
http://amzn.to/XRm7M4

Mind Your Puzzles: Collection Of Volumes 1 To 3
https://amzn.to/2mMdrJr
A collection of 3 books:
"Math Puzzles Volume 1" rated 4.4/5 stars on 138 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 45 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.3/5 stars on 38 reviews
http://amzn.to/1NKbGlp

2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter.

My Blog
https://mindyourdecisions.com/blog/

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https://teespring.com/stores/mind-your-decisions

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https://www.patreon.com/mindyourdecisions

Press
https://mindyourdecisions.com/blog/press