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QillerDaemon wrote: ↑Fri Aug 18, 2023 6:28 pm

Animal wrote: ↑Fri Aug 18, 2023 5:30 pm I am going to have to argue this point. Let's just simply talk about one card. The "K" card. In your explanation, you say that you don't have to turn it over to figure out if the rule has been broken. But let's say there is a "D" on the other side of the card.

"A card manufacturer makes a set of cards that have a letter on one side of a card and a number on the other side."

That's a given from the original problem. All cards have one letter on one side and one number on the other side.

No card is going to have two letters or two numbers on both sides of each card.

I would still submit that if a card printer can make a mistake on one rule (failing to put a 3 on the other side of a D) then he can also make a mistake printing a letter on the back of a letter. And you can only be sure that he didn't make that mistake by turning over the K to make sure there isn't a D on the other side.

25%

peterosehaircut wrote: ↑Mon Sep 18, 2023 4:20 am25%

if 25% is the right answer and there are two choices that are 25%, then wouldn't there be a 50% random chance of choosing the right one?

Animal wrote: ↑Mon Sep 18, 2023 1:14 pm

peterosehaircut wrote: ↑Mon Sep 18, 2023 4:20 am25%

if 25% is the right answer and there are two choices that are 25%, then wouldn't there be a 50% random chance of choosing the right one?

I agree, the correct answer can be chance B alone, or chances A and C together. Or both answers.

Three circles of equal circumference sit co-linear and tangent. A line is drawn from the center of the first circle, through the second circle, and tangent to the third circle. What is the length of the chord made by the line going through the second circle? If it helps, assume the circumference of each circle is 10π.

A right triangle ABC is drawn with perimeter = 336 units and area = 3360 units². Sides c > b > a. What are the lengths of the sides of the triangle?
(hint: set up a system of three equations and substitute between them)

QillerDaemon wrote: ↑Thu Mar 07, 2024 3:44 pm A right triangle ABC is drawn with perimeter = 336 units and area = 3360 units². Sides c > b > a. What are the lengths of the sides of the triangle?
(hint: set up a system of three equations and substitute between them)

a=48
b=140
c=148

Solve: 6 + f(x) = 2f(-x) + 3x²*INT(from -1 to +1)f(t)dt

To clarify, "3x²*INT(from -1 to +1)f(t)dt" means 3x² times the integral from -1 to 1 of f(t)dt.
Cuz I don't know how to make the cute skinny integral "S" sign.

Exam question from a recent Oxford math entrance test. 96% of the test takers could not solve it.

QillerDaemon wrote: ↑Tue Jul 09, 2024 1:36 am Solve: 6 + f(x) = 2f(-x) + 3x²*INT(from -1 to +1)f(t)dt

To clarify, "3x²*INT(from -1 to +1)f(t)dt" means 3x² times the integral from -1 to 1 of f(t)dt.
Cuz I don't know how to make the cute skinny integral "S" sign.

Exam question from a recent Oxford math entrance test. 96% of the test takers could not solve it.

Animal says hold my Pabst ....

Well, the integral of f(t)dt from 1 to -1 would be t^2/2 + t^2/2 which would be = 1. So, all of that equals 1.

You are then left with 6+y = -2y +3x^2

Which reduces to y = x^2 - 2 or f(x) = x^2 - 2

A rectangle of unknown dimensions is drawn, then inside the rectangle is drawn a circle of unknown radius that does not touch the rectangle.

From each internal corner of the rectangle is drawn a line segment which touches a point tangent to the circle. The lengths of three of these line segments is known, but not the fourth; the known segments are 10 units, 34 units and 85 units (for the sake of this problem). Calculate the length of the unknown line segment.

edit - I realize now that the problem's description is quite vague in one detail: the line segment from the corner could go tangent on one side of the circle or the other. Unless the segments are consistent on how they extend to the circle, the problem has no real solution, or a solution dependent on how the circles become tangent. So the line segments are tangent in a circular way in a right-hand direction, this is so the segments can't ever actual cross each other.

60

I don't have the time at the moment to attempt it, but i would start with this.

For each corner (say A, B, C, D) you have created a right triangle like this:

Let's say A has the 10 unit length that is tangental to the circle. We know a tangental segment hits a circle at 90 degrees to the radius. So we have a right Triangle A that has one side of 10 and one side of r. So the remaining side is the distance from the centerpoint of the circle to the corner A. That distance is A^2 = 10^2 + r^2. Now, you know that same information for two of the other corners. With r^2 being the common distance in each. And that would give you a way to find the two sides of the rectangle. Working backward with the same thing you could find the length of D.

That would take some time, though.

Prove:

1³ + 5³ + 3³ = 153

16³ + 50³ + 33³ = 165033

166³ + 500³ + 333³ = 166500333

1666³ + 5000³ + 3333³ = 166650003333

and so on.

this seems so narcissistic.

Animal wrote: ↑Thu May 29, 2025 10:01 pm this seems so narcissistic.

What do you mean? I thought it was an interesting problem. And it's not like those "real" math proofs with lots of weird words and symbols. It's actually pretty easy as long as you focus on the main problem (showing that both sides reduce to the same expression) and don't make a bad math boo-boo.

QillerDaemon wrote: ↑Fri May 30, 2025 1:11 pm

Animal wrote: ↑Thu May 29, 2025 10:01 pm this seems so narcissistic.

What do you mean? I thought it was an interesting problem. And it's not like those "real" math proofs with lots of weird words and symbols. It's actually pretty easy as long as you focus on the main problem (showing that both sides reduce to the same expression) and don't make a bad math boo-boo.

its literally a narcisstic math problem. there are a finite number of narcissistic numbers and 153 just happens to be one of them. its also interesting to learn why the number of them is finite.

Animal wrote: ↑Fri May 30, 2025 1:32 pm its literally a narcisstic math problem. there are a finite number of narcissistic numbers and 153 just happens to be one of them. its also interesting to learn why the number of them is finite.

Ah, I get ya now! I was not familiar with that term, to be honest. Got led down a rabbit hole googling that term.