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This problem is tougher than it looks!

Make 24 from the numbers 3, 3, 8, 8. https://downsfiles245.weebly.com/interactive-slot-games.html.

You can only use the operations + – × ÷ ().

You have to use all four numbers (the digit 3 two times and the digit 8 two times). There are no tricks here!

Can you figure it out? Watch the video for a solution.

Update: Thanks PopSugar for featuring this video!
https://www.popsugar.com/news/Math-Brain-Teaser-YouTube-44834174

Or keep reading.
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'All will be well if you use your mind for your decisions, and mind only your decisions.' Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.

3/8 Inch To Mm

Home Inventory 3 8 24 Months

Home Inventory 3 8 24 Tractor Tire

(This was transcribed quickly after I made the video–please let me know if there are any typos/errors and I will correct them, thanks).

This is actually a pretty tricky problem! Out of all possible combinations, there is only one solution.

Answer

Obviously 8 × 3 = 24, but you need to use all four numbers. So how you can you do that?

In this situation, a mathematician thinks about transforming the problem into another one. If we could make 8 from 8, 8, 3, then we would be done, since if f(8, 8, 3) = 8, then f(8, 8, 3) × 3 = 8 × 3 = 24.

Similarly, we could find solutions if we could solve any of these cases:

if f(8, 8, 3) = 8, then f(8, 8, 3) × 3 = 8 × 3 = 24

if f(8, 8, 3) = 1/8, then 3/f(8, 8, 3) = 3/(1/8) = 24

if f(3, 3, 8) = 3, then 8 × f(3, 3, 8) = 8 × 3 = 24

if f(3, 3, 8) = 1/3, then 8/f(3, 3, 8) = 8/(1/3) = 24 Wirecast pro 13 1 0.

You can play around with the numbers, and eventually you can find a clever way to make 1/3 from 3, 3, 8:

3 – 8/3 = 9/3 – 8/3 = 1/3

So that leads to the incredible answer:

8/(3 – 8/3) = 24

And that’s the only way you can arrange these numbers to make 24.

The solution is hard for three reasons. First, it requires two divisions and fractions. Second, it is the only solution out of all possible combinations. Third, the solution is challenging for computer programs because evaluating 3 – 8/3 = 1/3 requires special care to avoid floating point and rounding errors.

So there you go, that’s the answer to one of the hardest make 24 puzzles. Did you figure it out?

Further reading
This website tested that 3, 3, 8, 8 has only 1 unique solution.
http://www.4nums.com/game/difficulties/ Wolfrun slot machine.

Mark Dominus, on The Universe of Discourse, wrote a 3 part series about the challenges in writing a computer program to solve these kinds of puzzles. They are worth a read!

Other creative solutions using factorial, logarithms, cube roots, etc.
https://www.mathsisfun.com/puzzles/24-from-8-8-3-3-solution.html

How to find the solutions for 24 using computer code
https://www.codeproject.com/Articles/28435/The-Puzzle