# Fraction calculator: 3 1/8 + 2 3/8

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Posted April 9, 2018 By Presh Talwalkar. Read about me, or gmail me.

This problem is tougher than it looks!

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

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

You have sầu lớn 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 đoạn Clip for a solution.

**Harder Than It Looks! Can You Make 24 From 3, 3, 8, 8?**

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

**Or keep reading. . ."All will be well if you use your mind for your decisions, & mind only your decisions." Since 2007, I have sầu devoted my life to lớn sharing the joy of game theory & mathematics. aiesec-unwe.net now has over 1,000 không tính phí articles with no ads thanks to community support! Help out & get early access khổng lồ posts with a pledge on Patreon.**

**. . . . . . M I N D . Y O U R . D E C I S I O N S . Phường U Z Z L E . . . . Answer To Make 10 From 3, 3, 8, 8**

(This was transcribed quickly after I made the video–please let me know if there are any typos/errors và 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 lớn use all four numbers. So how you can you bởi 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 sầu 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

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

3 – 8/3 = 9/3 – 8/3 = 1/3

So that leads khổng lồ the incredible answer:

8/(3 – 8/3) = 24

And that’s the only way you can arrange these numbers lớn 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 khổng lồ avoid floating point & rounding errors.

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So there you go, that’s the answer to lớn 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/**

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

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

**https://blog.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-8-8-3-3-solution.html**

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

### PRESH TALWALKAR

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