This Problem Stumped Vietnamese Students - Solution To Viral Puzzler
- 6 years ago
This problem was asked to 3rd graders (8 year olds) in Vietnam. Can you figure it out? Place the numbers 1 to 9, using each number once, to make a valid equation. In this video I explain how you can solve this problem logically.\r
\r
UPDATE: Ive posted all 136 solutions, at the end of this description, found by testing every possibility. What that means is I used a spreadsheet to list out all 9! = 362,880 possibilities, evaluated each expression, and then found out which ones equaled 66.\r
\r
Sources\r
VN Express (Vietnamese) \r
\r
Via The Guardian (Alex Bellos) \r
\r
Connect on social media\r
My Blog: \r
Twitter: \r
Books: \r
Facebook: \r
Google+: \r
Pinterest: \r
Tumblr: \r
Instagram: \r
Patreon: \r
\r
Newsletter (sent about 2 times a year): \r
\r
The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) \r
\r
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 4.5/5 stars on 11 reviews. \r
\r
**FULL LIST OF ANSWERS**\r
\r
The numbers are to be placed in the grid from left to right. For example, the first set of numbers\r
\r
1 2 6 4 7 8 3 5 9\r
\r
means\r
\r
1+13*2/6+4+12*7-8-11+3*5/9-10 = 66\r
\r
So here are all 136 solutions. As stated in the video, each answer can really be written in 4 different ways when you exchange the first two numbers added or the last two numbers being multiplied. So what we have is 34 distinct equations that can be written in 4 equivalent ways.\r
\r
1 2 6 4 7 8 3 5 9\r
1 2 6 4 7 8 5 3 9\r
1 3 2 9 5 6 4 7 8\r
1 3 2 9 5 6 7 4 8\r
1 3 2 4 5 8 7 9 6\r
1 3 2 4 5 8 9 7 6\r
1 3 4 7 6 5 9 2 8\r
1 3 4 7 6 5 2 9 8\r
1 3 6 2 7 9 4 5 8\r
1 3 6 2 7 9 5 4 8\r
1 3 9 4 7 8 5 2 6\r
1 3 9 4 7 8 2 5 6\r
1 4 8 2 7 9 5 3 6\r
1 4 8 2 7 9 3 5 6\r
1 5 2 8 4 7 9 3 6\r
1 5 2 8 4 7 3 9 6\r
1 5 2 3 4 8 7 9 6\r
1 5 2 3 4 8 9 7 6\r
1 5 3 9 4 2 7 8 6\r
1 5 3 9 4 2 8 7 6\r
1 8 3 7 4 5 2 6 9\r
1 8 3 7 4 5 6 2 9\r
1 9 6 4 5 8 7 3 2\r
1 9 6 4 5 8 3 7 2\r
1 9 6 7 5 2 4 3 8\r
1 9 6 7 5 2 3 4 8\r
2 1 4 3 7 9 5 6 8\r
2 1 4 3 7 9 6 5 8\r
2 3 6 1 7 9 4 5 8\r
2 3 6 1 7 9 5 4 8\r
2 4 8 1 7 9 3 5 6\r
2 4 8 1 7 9 5 3 6\r
2 6 9 8 5 1 4 7 3\r
2 6 9 8 5 1 7 4 3\r
2 8 6 9 4 1 5 7 3\r
2 8 6 9 4 1 7 5 3\r
2 9 6 3 5 1 7 4 8\r
2 9 6 3 5 1 4 7 8\r
3 1 4 2 7 9 5 6 8\r
3 1 4 2 7 9 6 5 8\r
3 2 8 6 5 1 9 7 4\r
3 2 8 6 5 1 7 9 4\r
3 2 1 5 4 7 8 9 6\r
3 2 1 5 4 7 9 8 6\r
3 2 4 8 5 1 7 9 6\r
3 2 4 8 5 1 9 7 6\r
3 5 2 1 4 8 7 9 6\r
3 5 2 1 4 8 9 7 6\r
3 6 4 9 5 8 7 1 2\r
3 6 4 9 5 8 1 7 2\r
3 9 2 8 1 5 7 6 4\r
3 9 2 8 1 5 6 7 4\r
3 9 6 2 5 1 4 7 8\r
3 9 6 2 5 1 7 4 8\r
4 2 6 1 7 8 5 3 9\r
4 2 6 1 7 8 3 5 9\r
4 3 9 1 7 8 2 5 6\r
4 3 9 1 7 8 5 2 6\r
4 3 2 1 5 8 7 9 6\r
4 3 2 1 5 8 9 7 6\r
4 9 6 1 5 8 3 7 2\r
4 9 6 1 5 8 7 3 2\r
5 1 2 9 6 7 3 4 8\r
5 1 2 9 6 7 4 3 8\r
5 2 1 3 4 7 8 9 6\r
5 2 1 3 4 7 9 8 6\r
5 3 1 7 2 6 8 9 4\r
5 3 1 7 2 6 9 8 4\r
5 4 8 9 6 7 1 3 2\r
5 4 8 9 6 7 3 1 2\r
5 4 1 9 2 7 3 8 6\r
5 4 1 9 2 7 8 3 6\r
5 7 2 8 3 9 6 1 4\r
5 7 2 8 3 9 1 6 4\r
5 9 3 6 2 1 7 8 4\r
5 9 3 6 2 1 8 7 4\r
6 2 8 3 5 1 9 7 4\r
6 2 8 3 5 1 7 9 4\r
6 3 1 9 2 5 7 8 4\r
6 3 1 9 2 5 8 7 4\r
6 9 3 5 2 1 7 8 4\r
6 9 3 5 2 1 8 7 4\r
7 1 4 9 6 5 3 2 8\r
7 1 4 9 6 5 2 3 8\r
7 2 8 9 6 5 3 1 4\r
7 2 8 9 6 5 1 3 4\r
7 3 2 8 5 9 6 1 4\r
7 3 2 8 5 9 1 6 4\r
7 3 4 1 6 5 9 2 8\r
7 3 4 1 6 5 2 9 8\r
7 3 1 5 2 6 9 8 4\r
7 3 1 5 2 6 8 9 4\r
7 5 2 8 4 9 1 3 6\r
7 5 2 8 4 9 3 1 6\r
7 6 4 8 5 9 3 1 2\r
7 6 4 8 5 9 1 3 2\r
7 8 3 1 4 5 2 6 9\r
7 8 3 1 4 5 6 2 9\r
7 9 6 1 5 2 3 4 8\r
7 9 6 1 5 2 4 3 8\r
8 2 4 3 5 1 7 9 6\r
8 2 4 3 5 1 9 7 6\r
8 3 2 7 5 9 1 6 4\r
8 3 2 7 5 9 6 1 4\r
8 5 2 1 4 7 9 3 6\r
8 5 2 1 4 7 3 9 6\r
8 5 2 7 4 9 1 3 6\r
8 5 2 7 4 9 3 1 6\r
8 6 4 7 5 9 1 3 2\r
8 6 4 7 5 9 3 1 2\r
8 6 9 2 5 1 4 7 3\r
8 6 9 2 5 1 7 4 3\r
8 7 2 5 3 9 6 1 4\r
8 7 2 5 3 9 1 6 4\r
8 9 2 3 1 5 6 7 4\r
8 9 2 3 1 5 7 6 4\r
9 1 2 5 6 7 3 4 8\r
9 1 2 5 6 7 4 3 8\r
9 1 4 7 6 5 2 3 8\r
9 1 4 7 6 5 3 2 8\r
9 2 8 7 6 5 3 1 4\r
9 2 8 7 6 5 1 3 4\r
9 3 1 6 2 5 7 8 4\r
9 3 1 6 2 5 8 7 4\r
9 3 2 1 5 6 4 7 8\r
9 3 2 1 5 6 7 4 8\r
9 4 8 5 6 7 1 3 2\r
9 4 8 5 6 7 3 1 2\r
9 4 1 5 2 7 8 3 6\r
9 4 1 5 2 7 3 8 6\r
9 5 3 1 4 2 7 8 6\r
9 5 3 1 4 2 8 7 6\r
9 6 4 3 5 8 1 7 2\r
9 6 4 3 5 8 7 1 2\r
9 8 6 2 4 1 5 7 3\r
9 8 6 2 4 1 7 5 3
\r
UPDATE: Ive posted all 136 solutions, at the end of this description, found by testing every possibility. What that means is I used a spreadsheet to list out all 9! = 362,880 possibilities, evaluated each expression, and then found out which ones equaled 66.\r
\r
Sources\r
VN Express (Vietnamese) \r
\r
Via The Guardian (Alex Bellos) \r
\r
Connect on social media\r
My Blog: \r
Twitter: \r
Books: \r
Facebook: \r
Google+: \r
Pinterest: \r
Tumblr: \r
Instagram: \r
Patreon: \r
\r
Newsletter (sent about 2 times a year): \r
\r
The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4/5 stars on 23 reviews) \r
\r
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 4.5/5 stars on 11 reviews. \r
\r
**FULL LIST OF ANSWERS**\r
\r
The numbers are to be placed in the grid from left to right. For example, the first set of numbers\r
\r
1 2 6 4 7 8 3 5 9\r
\r
means\r
\r
1+13*2/6+4+12*7-8-11+3*5/9-10 = 66\r
\r
So here are all 136 solutions. As stated in the video, each answer can really be written in 4 different ways when you exchange the first two numbers added or the last two numbers being multiplied. So what we have is 34 distinct equations that can be written in 4 equivalent ways.\r
\r
1 2 6 4 7 8 3 5 9\r
1 2 6 4 7 8 5 3 9\r
1 3 2 9 5 6 4 7 8\r
1 3 2 9 5 6 7 4 8\r
1 3 2 4 5 8 7 9 6\r
1 3 2 4 5 8 9 7 6\r
1 3 4 7 6 5 9 2 8\r
1 3 4 7 6 5 2 9 8\r
1 3 6 2 7 9 4 5 8\r
1 3 6 2 7 9 5 4 8\r
1 3 9 4 7 8 5 2 6\r
1 3 9 4 7 8 2 5 6\r
1 4 8 2 7 9 5 3 6\r
1 4 8 2 7 9 3 5 6\r
1 5 2 8 4 7 9 3 6\r
1 5 2 8 4 7 3 9 6\r
1 5 2 3 4 8 7 9 6\r
1 5 2 3 4 8 9 7 6\r
1 5 3 9 4 2 7 8 6\r
1 5 3 9 4 2 8 7 6\r
1 8 3 7 4 5 2 6 9\r
1 8 3 7 4 5 6 2 9\r
1 9 6 4 5 8 7 3 2\r
1 9 6 4 5 8 3 7 2\r
1 9 6 7 5 2 4 3 8\r
1 9 6 7 5 2 3 4 8\r
2 1 4 3 7 9 5 6 8\r
2 1 4 3 7 9 6 5 8\r
2 3 6 1 7 9 4 5 8\r
2 3 6 1 7 9 5 4 8\r
2 4 8 1 7 9 3 5 6\r
2 4 8 1 7 9 5 3 6\r
2 6 9 8 5 1 4 7 3\r
2 6 9 8 5 1 7 4 3\r
2 8 6 9 4 1 5 7 3\r
2 8 6 9 4 1 7 5 3\r
2 9 6 3 5 1 7 4 8\r
2 9 6 3 5 1 4 7 8\r
3 1 4 2 7 9 5 6 8\r
3 1 4 2 7 9 6 5 8\r
3 2 8 6 5 1 9 7 4\r
3 2 8 6 5 1 7 9 4\r
3 2 1 5 4 7 8 9 6\r
3 2 1 5 4 7 9 8 6\r
3 2 4 8 5 1 7 9 6\r
3 2 4 8 5 1 9 7 6\r
3 5 2 1 4 8 7 9 6\r
3 5 2 1 4 8 9 7 6\r
3 6 4 9 5 8 7 1 2\r
3 6 4 9 5 8 1 7 2\r
3 9 2 8 1 5 7 6 4\r
3 9 2 8 1 5 6 7 4\r
3 9 6 2 5 1 4 7 8\r
3 9 6 2 5 1 7 4 8\r
4 2 6 1 7 8 5 3 9\r
4 2 6 1 7 8 3 5 9\r
4 3 9 1 7 8 2 5 6\r
4 3 9 1 7 8 5 2 6\r
4 3 2 1 5 8 7 9 6\r
4 3 2 1 5 8 9 7 6\r
4 9 6 1 5 8 3 7 2\r
4 9 6 1 5 8 7 3 2\r
5 1 2 9 6 7 3 4 8\r
5 1 2 9 6 7 4 3 8\r
5 2 1 3 4 7 8 9 6\r
5 2 1 3 4 7 9 8 6\r
5 3 1 7 2 6 8 9 4\r
5 3 1 7 2 6 9 8 4\r
5 4 8 9 6 7 1 3 2\r
5 4 8 9 6 7 3 1 2\r
5 4 1 9 2 7 3 8 6\r
5 4 1 9 2 7 8 3 6\r
5 7 2 8 3 9 6 1 4\r
5 7 2 8 3 9 1 6 4\r
5 9 3 6 2 1 7 8 4\r
5 9 3 6 2 1 8 7 4\r
6 2 8 3 5 1 9 7 4\r
6 2 8 3 5 1 7 9 4\r
6 3 1 9 2 5 7 8 4\r
6 3 1 9 2 5 8 7 4\r
6 9 3 5 2 1 7 8 4\r
6 9 3 5 2 1 8 7 4\r
7 1 4 9 6 5 3 2 8\r
7 1 4 9 6 5 2 3 8\r
7 2 8 9 6 5 3 1 4\r
7 2 8 9 6 5 1 3 4\r
7 3 2 8 5 9 6 1 4\r
7 3 2 8 5 9 1 6 4\r
7 3 4 1 6 5 9 2 8\r
7 3 4 1 6 5 2 9 8\r
7 3 1 5 2 6 9 8 4\r
7 3 1 5 2 6 8 9 4\r
7 5 2 8 4 9 1 3 6\r
7 5 2 8 4 9 3 1 6\r
7 6 4 8 5 9 3 1 2\r
7 6 4 8 5 9 1 3 2\r
7 8 3 1 4 5 2 6 9\r
7 8 3 1 4 5 6 2 9\r
7 9 6 1 5 2 3 4 8\r
7 9 6 1 5 2 4 3 8\r
8 2 4 3 5 1 7 9 6\r
8 2 4 3 5 1 9 7 6\r
8 3 2 7 5 9 1 6 4\r
8 3 2 7 5 9 6 1 4\r
8 5 2 1 4 7 9 3 6\r
8 5 2 1 4 7 3 9 6\r
8 5 2 7 4 9 1 3 6\r
8 5 2 7 4 9 3 1 6\r
8 6 4 7 5 9 1 3 2\r
8 6 4 7 5 9 3 1 2\r
8 6 9 2 5 1 4 7 3\r
8 6 9 2 5 1 7 4 3\r
8 7 2 5 3 9 6 1 4\r
8 7 2 5 3 9 1 6 4\r
8 9 2 3 1 5 6 7 4\r
8 9 2 3 1 5 7 6 4\r
9 1 2 5 6 7 3 4 8\r
9 1 2 5 6 7 4 3 8\r
9 1 4 7 6 5 2 3 8\r
9 1 4 7 6 5 3 2 8\r
9 2 8 7 6 5 3 1 4\r
9 2 8 7 6 5 1 3 4\r
9 3 1 6 2 5 7 8 4\r
9 3 1 6 2 5 8 7 4\r
9 3 2 1 5 6 4 7 8\r
9 3 2 1 5 6 7 4 8\r
9 4 8 5 6 7 1 3 2\r
9 4 8 5 6 7 3 1 2\r
9 4 1 5 2 7 8 3 6\r
9 4 1 5 2 7 3 8 6\r
9 5 3 1 4 2 7 8 6\r
9 5 3 1 4 2 8 7 6\r
9 6 4 3 5 8 1 7 2\r
9 6 4 3 5 8 7 1 2\r
9 8 6 2 4 1 5 7 3\r
9 8 6 2 4 1 7 5 3