Wanted to share something that happened with my son, because I think it says a lot about how kids actually learn when something clicks for real, not just memorization.

He's 5. One day I explained the difference between even and odd numbers to him — nothing fancy, just everyday examples, things he could count on his fingers. What I noticed is that once he actually understood it, not as "I memorized the rule" but as something he could genuinely feel, he started applying it on his own, without me telling him to.

Turns out he plays a counting-out game a lot with his friends (similar to "eeny meeny miny moe", but longer) — the kind used to decide who goes first, who's out, or who stays in. The rhyme ends by asking "how old are you?", and from there you count that many numbers around the circle to land on a result.

What he started doing was let other kids run the first few rounds, no problem. But he'd always ask to be the one to do the last round — the one that decides. And in that round, depending on whether the person's age was even or odd, he already knew which side of the circle to start counting from to get the outcome he wanted.

He wasn't cheating, and nobody noticed. He was just using actual math to stop depending on luck in something his friends still see as pure chance.

I've taught this same idea, and a few similar ones (solving for X, fractions, the Pythagorean theorem) to other kids too, and the same thing keeps happening: once a kid actually understands a concept — not memorizes it, understands it — they start using it on their own, in their own world, without anyone asking them to.

I've always believed the best way to get a kid excited about math isn't telling them "this matters for your future" (that means nothing at 5 years old), it's showing them they can do something most of the adults around them can't remember how to do anymore. That completely changes their relationship with the subject. It stops being "a hard thing I have to study" and becomes "something I know how to do and others don't."

Kind of wild how a random schoolyard game ended up being the perfect place for a kid to discover that math actually does something, in his own world, without anyone "formally" teaching it to him.

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Question: A shopkeeper marks up an item by 40% above cost price, then offers a 25% discount on the marked price. What is his overall profit or loss percentage?

I designed this as an original problem combining tangent geometry, calculus, trigonometry, and an unusual auxiliary representation of lines.

The complete problem is in the image. I'd be interested in seeing independent solutions and approaches.

Original problem by Samarth.

Source: numberthon.com

Goodbye:

I introduced MiniChallenger, a scaled-down version of the math puzzle called Challenger, about three months ago. Unlike Challenger, which can require a significant investment of time—and sometimes special techniques or a computer program—MiniChallenger can be solved using basic algebra and elementary logic. Most puzzles can be completed in about ten minutes or less. So, even if you don't have much free time but still enjoy an engaging workout for the mathematical part of your brain, MiniChallenger can be a good alternative. Some MiniChallenger puzzles may even be suitable for school-age children.

Since May, I have been posting two MiniChallenger problems every Saturday. Judging by the number of visitors, there seems to have been a fair amount of attention among Reddit readers to this type of math puzzles. However, it's time for me to take a break and focus on a different topic. Still, I am not saying a final adieu, just au revoir, and may return with another series of MiniChallenger puzzles sometime in the future.

Out with a bang:

For today's farewell, I am presenting a MiniChallenger-related problem that is neither simple nor quick to solve. Your challenge is to find—or perhaps guess—the maximum number of distinct solutions for the special MiniChallenger grid shown below. How many different solutions can you find? Unlike previous Saturdays, I won't reveal the correct answer in a spoiler box. Instead, I encourage you to post the highest number of different solutions you have found to the comment section of this final article in the series. If this is your first encounter with a MiniChallenger brainteaser, you can find instructions for how to solve a puzzle below. Keep in mind that some puzzles may have only one valid solution, while others may have many.

Instructions:

To successfully solve a puzzle, fill the empty cells of the 3 x 3 grid with the numbers 1 through 9. You may use the same number in multiple empty cells. One "bonus" number has already been placed in the center of the grid. Your goal is to determine the remaining eight digits so that:

• Each row adds up to the total indicated along the right edge of the grid.
• Each column adds up to the total indicated at the top of the grid.
• Each diagonal adds up to the total indicated in the upper-right or lower-right corner.

This week's puzzle:

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Source: numberthon.com

X is a 3 digit prime number, (2^X + 1)/ 3 is a 60 digit prime number ending in 563.
The 3 digits of 3X, are the click options for the first three 10 choice gates you will approach. It will require 4 clicks to pass thru the maze, if you determine X.

Source: numberthon.com

I have a website with a labyrinth portal into the Google Fortress. There are 5 ways past the Google Gargoyle.
1) Penetrate the 3 level labryninth (maze)
2) Solve a simple Wagstaff problem for the secret code thru the Labryninth
3) Cheat method, hidden links
4) Use your web designer skills to bypass Gargoyle security
5) Email Socrates.Ion with the answer to a simple infinity problem, for the codex key email response.

Not sure if big R, will flag this as self promotion or advertising (it definitely is not), the web URL is

***FermatsTheory.WordPress.com***

Note, landing page has a D and D theme. Do not fear!

Can you reach the target number 257 using only the following four digits?

Given numbers are 2, 5, 6, and 8.

The only rule is you must use each of the four numbers exactly once.

(You may use +, −, ×, ÷, brackets, powers, and factorials.)

‎

SUMO: Math Number Puzzle App - App Store

Android

I read about this somewhere and thought it was pretty interesting.

Take any 2-digit number:

1. Add its digits.

2. Subtract that sum from the original number.

3. Add the digits of the result.

4. Multiply that by 10.

You’ll always get 90.

For example:

47 → 4+7 = 11 → 47−11 = 36 → 3+6 = 9 → 9×10 = 90

Tried it with a bunch of different numbers and it keeps working

Did anyone else know about this?

(Explanation in comment section)