IQ test sample patterns

C

Chiquitain

I was solving the sample problems for my school's IQ society and there are some I don't get. Since all I get is a final score, I wanted to ask puzzling if someone might be able to make things clearer. For the problem that I've answered I'm writing down the answer and explanation below. I'm not sure if it's right though.

'https://i.stack.imgur.com/Pndg3.png']
Pndg3.png
[/URL] 'https://i.stack.imgur.com/ZcCLR.png']
ZcCLR.png
[/URL] 'https://i.stack.imgur.com/N9pRp.png']
N9pRp.png
[/URL] 'https://i.stack.imgur.com/HUaeE.png']
HUaeE.png
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Unreplied Threads

Chilis that taste like habanero

  • Emil
  • Social
  • Replies: 0
I like the fruity taste of habanero a lot (the red ones if that matters). But I usually get stomach pains after eating them (not that it stops me). Are there any chilis that taste similar to habanero but burns less/are easier on the stomach/have less scoville rating?

Terminal singularities of fibers vs total space

Suppose $f\colon X \to Y$ is a flat map of complex varieties (or more generally DM stacks?). Suppose every fiber has at most terminal singularities and that $Y$ is smooth. Under what conditions is it known whether $X$ also has at most terminal singularities?

Basically, I'm wondering if there are results similar to Elkik's theorem from 1978 for rational singularities (Elkik's theorem also implies that if $X$ is a locally complete intersection scheme, then the fibers having at most canonical singularities implies $X$ does as well).

Can every positive integer eventually be expressed in this form?

$$a=\sum_{k=0}^c(k+2)^{s_k}$$ Can every positive integer eventually be expressed in this form where $s_k\ge1$ and $c\ge1$?

My Take:
First, I'll figure out the conditions for an even/odd number
Since $k^n$ is odd when odd and even when even, $(2k+1)^n\equiv1$ mod $2$, $(2k)^n\equiv0$ mod $2$.
From this, you find that for $a$ to be even, $c=4n,4n+1$. Also, for $a$ to be odd, $c=4n-1,4n-2$.

I couldn't find anything other than this, but there is a high chance it is possible to find a proof for this statement.

Notes:
$1.$ I have found 8 numbers that cannot be expressed in this form $(1,3,6,10,12,18,24,30)$, and most are multiples of 6.
$2.$ I have checked up to $10000$ for any counterexample.

When can $RHom^\bullet_{A}(B/I^k\overset{L}{\otimes}_B A, A)$ be computed using formal completions?

Let $\varphi:B\to A$ be a ring homomorphism between Noetherian rings. Let $I\subset B$ be an ideal. Let $B^{\wedge}=\varprojlim_n B/I^n$ be the $I$-adic completion of $B$, and $A^{\wedge}=\varprojlim_n A/(A\cdot\varphi(I))^n$ be the $A\cdot\varphi(I)$-adic completion of $A$. Let $I^\wedge=B^\wedge\cdot I$.

Question: Is it true that for every $k\in \mathbb{Z}_{>0}$, the natural map induced by $\overset{L}{\otimes}_A A^\wedge=\otimes_A A^\wedge$ $$RHom^\bullet_{A}(B/I^k\overset{L}{\otimes}_B A, A)\to RHom^\bullet_{A^\wedge}(B^\wedge/(I^\wedge)^k\overset{L}{\otimes}_{B^\wedge} A^\wedge, A^\wedge)$$ is an isomorphism? If not, under what conditions (not assuming $A$ is flat over $B$), the map is an isomorphism?

Are circles required on the edge of the grid?

  • Will Octagon Gibson
  • Technology
  • Replies: 0
The image below is a puzzle from the FlowFree app:

enter image description here

The image below is my solution to the above puzzle:

enter image description here

The rules stated in the app are:

Drag to connect matching colors with pipe, creating a flow. Pair all colors, and cover the entire board with pipe to solve each puzzle. But watch out, pipes will break if they cross or overlap!


For the example puzzle, there are two colored circles on the edge of the grid (a blue circle and a red circle on the bottom edge).

My question is:

Does there exist a grid (not necessarily square) with a set of colored pairs of circles in the grid such that there are no colored circles on the edge of the grid and there is a unique solution that satisfies the app’s rules?

ST7735 driver IC connection with TFT DISPLAY

  • Sukhdarshan Vinayak
  • Physics
  • Replies: 0
I am a noob to electronics and thinking of using this 128x160 1.8 inch Color TFT LCD Display with ST7735 Controller SPI in my project. So, does the TFT Display come with a pre-programmed ST7735 Controller or do we have to program the Controller ourselves from designing the schematic to driver firmware? Or it comes with direct plug-and-play like pre-connected and we have to use the SPI pins like SDA, SCL, CLK, VCC, and GND of MCU to make the connection to the Display.

https://www.buydisplay.com/128x160-1-8-inch-color-tft-lcd-display-with-st7735-controller-spi

This is the link to the display I want to you for my project.

If we have to make the schematic for the ST7735 driver IC connection with TFT DISPLAY can you help me? in finding the proper resource for that also. I am using ESP32-S3 MCU to display the live video feed from the camera to TFT Display.

Thanks in advance for the help.

How to replace an 8-pin relay with a 10-pin relay?

  • Gerardo Felix
  • Physics
  • Replies: 0
I've been trying to reproduce the results of some experiments included in the Make: Electronics book by Charles Platt where 8-pin relays are used. The thing is that I haven't found DPDT 9V 8-pin relay as suggested in the book, and I only found 10-pin 9V relays. In the image below I show how the 8-pin relay is supposed to work and the schematics of the 10-pin relay I have.

Schematics of the 8 and 10 pin relays

What should I do with the 2 extra pins in my relay? Can someone help me understand how to connect the 10-pin relay to replace the 8-pin relay?
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