This Problem Stumped Vietnamese Students – Solution To Viral Puzzler


This Problem Stumped Vietnamese Students - Solution To Viral Puzzler

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.

UPDATE: I've 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.

Sources
VN Express (Vietnamese) http://vnexpress.net/tin-tuc/giao-duc/bai-toan-lop-3-lam-kho-ca-tien-si-3220186.html

Via The Guardian (Alex Bellos) http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/may/20/can-you-do-the-maths-puzzle-for-vietnamese-eight-year-olds-that-has-stumped-parents-and-teachers

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**FULL LIST OF ANSWERS**

The numbers are to be placed in the grid from left to right. For example, the first set of numbers

1 2 6 4 7 8 3 5 9

means

1+13*2/6+4+12*7-8-11+3*5/9-10 = 66

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.

1 2 6 4 7 8 3 5 9
1 2 6 4 7 8 5 3 9
1 3 2 9 5 6 4 7 8
1 3 2 9 5 6 7 4 8
1 3 2 4 5 8 7 9 6
1 3 2 4 5 8 9 7 6
1 3 4 7 6 5 9 2 8
1 3 4 7 6 5 2 9 8
1 3 6 2 7 9 4 5 8
1 3 6 2 7 9 5 4 8
1 3 9 4 7 8 5 2 6
1 3 9 4 7 8 2 5 6
1 4 8 2 7 9 5 3 6
1 4 8 2 7 9 3 5 6
1 5 2 8 4 7 9 3 6
1 5 2 8 4 7 3 9 6
1 5 2 3 4 8 7 9 6
1 5 2 3 4 8 9 7 6
1 5 3 9 4 2 7 8 6
1 5 3 9 4 2 8 7 6
1 8 3 7 4 5 2 6 9
1 8 3 7 4 5 6 2 9
1 9 6 4 5 8 7 3 2
1 9 6 4 5 8 3 7 2
1 9 6 7 5 2 4 3 8
1 9 6 7 5 2 3 4 8
2 1 4 3 7 9 5 6 8
2 1 4 3 7 9 6 5 8
2 3 6 1 7 9 4 5 8
2 3 6 1 7 9 5 4 8
2 4 8 1 7 9 3 5 6
2 4 8 1 7 9 5 3 6
2 6 9 8 5 1 4 7 3
2 6 9 8 5 1 7 4 3
2 8 6 9 4 1 5 7 3
2 8 6 9 4 1 7 5 3
2 9 6 3 5 1 7 4 8
2 9 6 3 5 1 4 7 8
3 1 4 2 7 9 5 6 8
3 1 4 2 7 9 6 5 8
3 2 8 6 5 1 9 7 4
3 2 8 6 5 1 7 9 4
3 2 1 5 4 7 8 9 6
3 2 1 5 4 7 9 8 6
3 2 4 8 5 1 7 9 6
3 2 4 8 5 1 9 7 6
3 5 2 1 4 8 7 9 6
3 5 2 1 4 8 9 7 6
3 6 4 9 5 8 7 1 2
3 6 4 9 5 8 1 7 2
3 9 2 8 1 5 7 6 4
3 9 2 8 1 5 6 7 4
3 9 6 2 5 1 4 7 8
3 9 6 2 5 1 7 4 8
4 2 6 1 7 8 5 3 9
4 2 6 1 7 8 3 5 9
4 3 9 1 7 8 2 5 6
4 3 9 1 7 8 5 2 6
4 3 2 1 5 8 7 9 6
4 3 2 1 5 8 9 7 6
4 9 6 1 5 8 3 7 2
4 9 6 1 5 8 7 3 2
5 1 2 9 6 7 3 4 8
5 1 2 9 6 7 4 3 8
5 2 1 3 4 7 8 9 6
5 2 1 3 4 7 9 8 6
5 3 1 7 2 6 8 9 4
5 3 1 7 2 6 9 8 4
5 4 8 9 6 7 1 3 2
5 4 8 9 6 7 3 1 2
5 4 1 9 2 7 3 8 6
5 4 1 9 2 7 8 3 6
5 7 2 8 3 9 6 1 4
5 7 2 8 3 9 1 6 4
5 9 3 6 2 1 7 8 4
5 9 3 6 2 1 8 7 4
6 2 8 3 5 1 9 7 4
6 2 8 3 5 1 7 9 4
6 3 1 9 2 5 7 8 4
6 3 1 9 2 5 8 7 4
6 9 3 5 2 1 7 8 4
6 9 3 5 2 1 8 7 4
7 1 4 9 6 5 3 2 8
7 1 4 9 6 5 2 3 8
7 2 8 9 6 5 3 1 4
7 2 8 9 6 5 1 3 4
7 3 2 8 5 9 6 1 4
7 3 2 8 5 9 1 6 4
7 3 4 1 6 5 9 2 8
7 3 4 1 6 5 2 9 8
7 3 1 5 2 6 9 8 4
7 3 1 5 2 6 8 9 4
7 5 2 8 4 9 1 3 6
7 5 2 8 4 9 3 1 6
7 6 4 8 5 9 3 1 2
7 6 4 8 5 9 1 3 2
7 8 3 1 4 5 2 6 9
7 8 3 1 4 5 6 2 9
7 9 6 1 5 2 3 4 8
7 9 6 1 5 2 4 3 8
8 2 4 3 5 1 7 9 6
8 2 4 3 5 1 9 7 6
8 3 2 7 5 9 1 6 4
8 3 2 7 5 9 6 1 4
8 5 2 1 4 7 9 3 6
8 5 2 1 4 7 3 9 6
8 5 2 7 4 9 1 3 6
8 5 2 7 4 9 3 1 6
8 6 4 7 5 9 1 3 2
8 6 4 7 5 9 3 1 2
8 6 9 2 5 1 4 7 3
8 6 9 2 5 1 7 4 3
8 7 2 5 3 9 6 1 4
8 7 2 5 3 9 1 6 4
8 9 2 3 1 5 6 7 4
8 9 2 3 1 5 7 6 4
9 1 2 5 6 7 3 4 8
9 1 2 5 6 7 4 3 8
9 1 4 7 6 5 2 3 8
9 1 4 7 6 5 3 2 8
9 2 8 7 6 5 3 1 4
9 2 8 7 6 5 1 3 4
9 3 1 6 2 5 7 8 4
9 3 1 6 2 5 8 7 4
9 3 2 1 5 6 4 7 8
9 3 2 1 5 6 7 4 8
9 4 8 5 6 7 1 3 2
9 4 8 5 6 7 3 1 2
9 4 1 5 2 7 8 3 6
9 4 1 5 2 7 3 8 6
9 5 3 1 4 2 7 8 6
9 5 3 1 4 2 8 7 6
9 6 4 3 5 8 1 7 2
9 6 4 3 5 8 7 1 2
9 8 6 2 4 1 5 7 3
9 8 6 2 4 1 7 5 3