8 8 8 8 3

This problem is tougher than it looks!

Make 24 from the numbers three, 3, 8, 8.

Y'all can just use the operations + – × ÷ ().

You have to use all four numbers (the digit iii two times and the digit 8 two times). In that location are no tricks here!

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

Harder Than Information technology Looks! Can You Brand 24 From 3, 3, 8, 8?

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

Or proceed reading.
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"All will be well if you apply your heed for your decisions, and listen only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over ane,000 complimentary articles with no ads thanks to community support! Assistance out and get early access to posts with a pledge on Patreon.

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Reply To Make x From 3, 3, eight, 8

(This was transcribed quickly subsequently 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 trouble! Out of all possible combinations, there is only one solution.

Answer

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

In this situation, a mathematician thinks nearly transforming the problem into some other one. If we could brand 8 from 8, 8, 3, then we would be done, since if f(eight, viii, 3) = 8, then f(8, 8, iii) × three = 8 × 3 = 24.

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

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

if f(8, eight, 3) = ane/8, then 3/f(8, 8, 3) = three/(ane/eight) = 24

if f(3, 3, viii) = 3, so eight × f(iii, three, eight) = 8 × 3 = 24

if f(3, 3, 8) = one/iii, so 8/f(three, three, 8) = 8/(one/3) = 24

You tin can play around with the numbers, and eventually you can discover a clever fashion to make 1/3 from three, 3, 8:

3 – 8/three = 9/3 – 8/iii = i/3

So that leads to the incredible answer:

eight/(iii – 8/iii) = 24

And that'due south the only fashion you can conform these numbers to make 24.

The solution is hard for iii reasons. First, information technology requires ii divisions and fractions. 2d, it is the simply solution out of all possible combinations. Third, the solution is challenging for computer programs because evaluating iii – 8/3 = 1/3 requires special care to avoid floating point and rounding errors.

Then there you go, that's the answer to ane of the hardest make 24 puzzles. Did you figure it out?

Farther reading
This website tested that 3, three, 8, 8 has only i unique solution.
http://world wide web.4nums.com/game/difficulties/

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

https://blog.plover.com/math/24-puzzle.html

https://weblog.plover.com/math/24-puzzle-2.html

https://blog.plover.com/math/24-puzzle-3.html

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

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

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