computer science – Throwing $K$ glass balls from tower – quadratic recurrence

Super famous related question: We have two identical glass balls, and a tower with 100 floors. We want to find the minimum floor from which the balls will break when dropped, in a minimal number of test throws.

Solution: Suppose we have $n$ throws to work with. What’s the maximum amount of floors we can cover with $n$ throws safely?

Suppose we throw the first ball from floor $n+1$ and it broke. Now we need to cover $n$ floors with $n-1$ throws of a single ball. That’s impossible, so instead we must throw the first ball from at most floor $n$ and it’s clear we should do that. In the best case, it doesn’t break (and so we checked the first $n$ floors) and now we need to throw from floor $n + (n-1)$, and so on.

So the maximum amount of floors we can check with $2$ balls is $n+(n-1)+(n-2) + dots + 1 = frac{n(n+1)}{2}$, we want this to be minimal as possible but greater than $100$, and the answer is $n=14$.

What would happen if we have $K$ balls?

The above solution hints at the direction, I believe. Denote $T(j)$ to be the maximum amount of floors we can cover safely with $j$ balls and $n$ throws. $T(1) = n$ obviously, we already saw $T(2) = frac{n(n+1)}{2}$.

Now I want to know $T(K)$. Going by the above logic, I can’t throw the first ball from floor $T(K-1) + 1$. Again I need to throw from $T(K-1)$, and then $T(K-1) + (T(K-1) – 1)$ and so on, and so

$T(K) = frac{1}{2}T^2(K-1) + frac{1}{2}T(K)$

This is a quadratic recurrence relation. How do we solve such beasts?

Dangers Of Transporting Big Glass Products

dnd 5e – What is the rarity of my homebrew Glass Sword?

I was writing up some magical weapons and had a fond remembrance of the “Glass Sword” from Ultima VII (apparently V/VI/IX as well). While I didn’t want to preserve the “save or die” aspect, I wanted to preserve a similar feel of “unusual, fragile, and deadly”, and came up with this:

Glass Sword

Weapon (longsword) (no attunement required)

Beautiful and deadly, it is as sharp as it is fragile. This sword deals 2d20 (11) slashing damage. Counts as magic for the purpose of piercing resistance or immunity. On a successful hit (whether or not damage is dealt) roll a d20 to see if the sword shatters – if it does, add an additional 2d20 + 10 (21) damage. The sword initially shatters on a roll of 5 or lower, but this increases by 1 with any successful attack.

Since it will survive for well under 4 hits on average, I believe it is best compared to consumable magical items (and the corresponding scrolls), e.g.:

  • (RARE) Necklace of fireballs – 4-9 instances of 8d6 (28) fire damage, or 0-1 of 14d6 (49)
  • (RARE) 4/5th level spell scroll (~30/40 damage, aoe)
  • (VERY RARE) 6/7/8th level spell scroll (~50/50/40 damage, aoe, various effects)
  • (LEGENDARY) 9th level spell scroll (~110 damage, aoe)

and seems to fall a bit short of Very Rare.

equipment recommendation – How do I photograph large appliances with glass doors for product showcasing?

In a reflective surface, the reflections are of the surrounding area.

1. The bigger the object the bigger space you need

So, in your case, you need a really big space clean, let’s say painted on white, like a photo studio.

Look how humungous and clean a photo studio can be. I think you need about the space to fit two or three cars.

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A 90° corner could work so you only need to fix two walls. A flat surface, not an industrial brick. You can put white ceramic mosaics in that zone.

2. Put the furniture in an angle

So you reflect what is on the side of the furniture, not what is behind you.

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If you use a wide lens, the elements that are reflected will appear smaller, which is not good because you need a bigger wall, so try to use a longer focal length and step back.

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3. You could “fake” a big room

Using big pieces of white fabric, 1.5 m width and like 2-10 m long. Use stretchy material like Lycra, a tripod, multiple shots, and 2-4 assistants.

Take two large rigid metal tubes aluminum or steel. Fix the fabric and use them as a big banner.

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Put the camera on a tripod, frame the product, concentrate the effort in protecting the reflection of one zone, let’s say the reflection of one door. Take one photo. And DO NOT MOVE THE CAMERA.

Protect the reflection on another door, and take another photo. Keep doing this. Until you have all the faces of the product taken.

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Use some more as a background.

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Composite the images in Photoshop or Gimp. Add more background later, focus only on the reflections and the immediate stuff behind the product.

4. Or as your company constructs metal frames

Make some big metal panels that can be covered with the stretchy cloth to have a portable studio room.

5. Make a 3D model of them

The shapes are pretty simple… you could model them quite easily.

Important note

Product photography is an art in itself. We are not focusing for now on how to properly lit the product, only to improve to some extent the resulting image.

If you want to push this to the next level we need to think in terms of light sources, which will turn some of your white fabric into light sources themselves, but that will not only complicate things for you, but it will take some years of expertise.

Photographing even small reflective objects are some of the trickiest things to photograph. You probably need to hire a photographer to have great images.

What is the terminology for a convex lens on a glass?

An example is a concave microscope slide.
I wonder if the opposite exists, then a convex lens that is part of the glass?
Is there a term for having glass around a lens / a lens on glass?
Thank you!

generate glass report based on combo box selection in vb

Visual code I have a form with 1 Button and 1 Combobox that has items loaded from different Reports. When selecting the combobox press button to search the report. but it sends me a memory error and indicates the report does not exist The code is:

Private Sub BtnTipoReporte_Click (sender As System.Object, e As System.EventArgs) Handles BtnTipoReporte.Click

    Dim rtp As New Reporte_Pagos

    If ComboReporte.Text = "REPORTE DE PAGOS" Then
       'CrystalReportViewer1.ReportSource = Application.StartupPath + "Reporte_Pagos.rtp"

        CrystalReportViewer1.ReportSource = rtp
    End If

Open the crystal report view but when loading another report it repeats the first report

dnd 5e: Can a fireball, a fragile glass jar, and many ball bearings make a "Claymore" type explosive device?

This answer assumes that the desired effect is "ball bearings / clay plus mine" and that ball of fire It was the best you could think of. I will offer that there is something else available if you allow other elements of the game as a solution set.

Exam question: How do we get animated object in the hands of the rogue, or in the hands of a fifth level group in general?

Option 1: Claymore with the assistant participating (risk of failure)

A parchment of animated object, a single use, with the risk that, since the Spell is of 5th level, and the magician is of 5th level and, therefore, can only use spells of up to 3rd level, the attempt may fail since the Possibility of scrolling not working. Rogue places ball bearings, magician molds animated object of the parchment, and if DC 15one The roll is made, the Claymore butcher shop proceeds as follows.

Option 2: Claymore for a 5th level arcane rogue

If your rogue is an Arcane Cheater, then he can use wands since at level 3 the rogue takes on the role of casting spells. Otherwise, the rogue needs to wait at level 13 to use magic devices. Your magician can use his fireballs for other challenges to the party. Or, the wizard can use the magic wand, like the previous scroll but without the possibility of failure.


  1. A wand generally requires tuning, and would need such a wand to arrive in loot / trade / treasure / whatever. This means that you would have to agree to offer a rare Magic item for your player at level 5. This might be early in terms of level / magic, but it's not too far from the box. (See DMG rarity guidelines for magic items / treasures, there are some rare items to play in Level 2, page 135; rare appears in character level "5th or above")

  2. Not all wands require tuning by a spellcaster, although the one I used as a model does. You can choose that the proposed wand requires tuning, but does not require "by a spellcaster" for any rogue to use. If you leave tuning as shown on the original wand, then the wizard could use it in any case.

Reskin the Binding Wand be the Animation wand

The Link Wand has 7 charges, and you can use 5 of them to cast the 5th level monster retention spell, or the level 2 retention person spell (2 charges). (1d6 recharge + 1 charge at dawn) Save spell / attack DC 17 (requires tuning by a spellcaster) (SRD p. 248)

It becomes an element of comparable power called

Animation wand that it has 7 charges; Casting Animated Item (5th level) uses five charges, casting Levitar (2nd level) uses two charges. (1d6 recharge + 1 charge at dawn) Save spell / attack DC 17 (Optional: requires tuning by a spellcaster)

Why animate objects?

Animate 5th level transmutation objects
Launch time: 1 action
Range: 120 ft Components: V, S
Duration: Concentration, up to 1 minute (This allows you to delay!)

{snip} Choose up to ten non-magic items within range that are not being used or transported.

I think we can safely call a ball that has a small object. 🙂

{snip} Tiny, +8 on hit, 1d4 + 4 damage (Table in spell description)
{snip} If you order an object to attack, it can make a single melee attack against a creature within 5 feet of it. Perform a hit attack with an attack bonus and blunt damage determined by its size.

Here's your Claymore:

  1. Place 10 ball bearings on the floor, in a bowl, in a helmet or whatever is suitable for your rogue.

  2. Use the wand to throw animated object and then (here is the delay part) when the time is right, order the ball bearings to attack. You have up to a minute, depending on how long it has been delayed. The text says that an object can attack a single creature, so this is both a "shotgun" and a claymore. However, you can get the "pattern" effect if, as a DM, you interpret the spell to allow each ball bearing to attack any creature within range … I can see that goes both ways for this spell application. . (You are already at home preparing a little, why not?)

The wand holder rolls 10 "to hit" rolls. For each bearing it hits it does 1d4 + 4 damage. A maximum possible of 10d4 + 40, but you will probably miss some … and if some critics, much better!

The above procedure makes the Claymore mine usable once per recharge cycle. (Unless d6 recharge cycle stinks)

  • Final caveat: As @Szega points out, one reading of this spell text is that
    the ball bearing can make an attack while your launcher / wand
    the wearer can focus on the spell. That would make this much more
    lethal than a "one shot explosion" as each ball bearing could attack
    for up to 10 rounds. If you feel that it is too powerful, you can
    reduce the number of rounds that ball bearings can attack, or you can go
    go ahead let it be impressive claymore butcher shop for that big bang of the
    adventure day / recharge. The limiting factor there is whether or not the rogue or wizard can stay focused. As players level up, opponents' HP will tend to better handle damage, which is part of why I made the above warning about rare items and character levels. (An offset is the most conservative approach.)

    Added levitate as a level 2 spell for the magic wand as it seems thematic to move things with magic. There is no need to be in the wand, and it could be removed without damaging the desired effect of a Claymore crafting method using what's available in the rulebook, with a slight tweak.

Note: I stole this idea from a player in our game whose magician does exactly this with ball bearings and animate objects. It is the eleventh level. Our DM rules that everyone attacks at once, what I like to call the "shotgun blast" effect. But "personal claymore" works well. 🙂

one From Spell Displacement (DMG):

If the spell is on your class's spell list but has a higher level than
normally you can throw, you must do a skill test using your
ability to cast spells to determine if you cast it successfully.
The CD equals 10 + the level of the spell. In a failed check, the spell
it disappears from the parchment without any other effect.

Apple Remote Desktop: switch between the red arrow and the magnifying glass as "remote cursor" in observation mode

I use Apple Remote Desktop (ARD) to provide remote assistance to various users on our LAN.

Sometimes I use the "observe" mode, this has always given me a magnifying glass that I could use as a cursor to zoom in on things on the user's screen.

Recently I was in a remote session in "observe" mode and instead of a magnifying glass I had a red arrow.

When I logged out and came back, again in "watch" mode the red arrow was gone and the magnifying glass was back.

Any ideas where / how I can toggle between the two?

Background I am running 10.14 (latest minor version) and I was connecting to a computer at 10.15 (latest minor version)

How to add magnifying glass zoom effect in full frame?

I need to add magnifying glass zoom effect in full-screen photoroma.enter the description of the image here

applications – glass magnifier application, only at fingertips

I'm looking for an application (maybe it never existed and I imagined it), but it's a screen magnifier that only enlarges a small circle around the tip of your finger, like the equivalent of a 5-letter word, ideal for enlarging specific words or areas of your screen, I think I saw it once (on the iPhone, maybe?), you just need to keep the tip of your finger on the screen for about 2 seconds, then a small circle appears above the tip of your finger that magnifies anything under it, and you can move it around your screen, and it disappears when you lift your finger, is there such a thing?

There is triple TAP, but it enlarges the entire screen and I don't want that.