A tower has 10 blocks. Each blocks height can be 2, 3,7, or 9. How many different possible heights?

[north pier]

What have you tried?

Just start trying it, then look for patterns later

There's no magic to a question like this.

I'm literally telling you how to solve it

You can pretend the possible block heights are 0,1,5,7

[severe tulip]

sorry man we dont do that here, if you have no intention on putting any effort on your part and trying to learn then look for answers someplace else.

[north pier]

You should show what you've done to get more specific help.

2+2+2+2+7=3+3+3+3+3

[eternal prairie]

Ah ofc.

Plz ellaborate, I dont understand

[hollow chasm]

i get only 480

surprisingly few

[hollow chasm]

@brazen edgeinteresting, how did you check?

[hollow chasm]

it's the 480 heights i got

could be important to you, so i sent just in case

[hollow chasm]

what no

it was compooted on a thingie

[hollow chasm]

personal computer

[manic ridge]

They probably wrote a program

[brazen edge]

im very stupid so dont be mad at me but this is kind of brute force dont you think?

isnt there some sort of equation for this

like maybe multiply all the possible numbers by 10

20, 30, 70, 90

and add all those up

that should be the max

i think im very wrong

or maybe wait

maybe you could split the 10?

theres max 10 right

4 possible numbers

oh wait the question was how many possible heights

not the heighest

im very stupid

sorry

i was confused for a sec cuz my brain just said "90" but i said that makes no sense

so yeah im dumb

sowwy

could it be as simple as 2 x 3 x 7 x 9 x 10 ?

thats 3780 btw

[brazen edge]

WAITTTT

COULD IT BE 2140????

i think i solved it

[jolly raptor]

can yu explain? I stumbled over this and now Im invested HAHAHA how did you solve it

doesnt seem right to me, dont u gotta do something with exponentials

Idk, 388 is a way too low number for a 97 brick tower with each brick having different hight combs

I failed statistics :,)

So idk

this is getting so complicated 🗿

yes

thank you I feel like my brain will die if I try to learn this, imma go back to my calculus but thank you for the explanation! I get the principle

[hollow chasm]

@brazen edgei can see how it makes sense if you have 2 types of bricks, i don;t know how you can extend to 3

i mean, if you have at most 2 types at the same time, you can count repeating heights from lcm of 6 and 15

hm

well nevermind i'll assume there's no way

no clue what you mean

[brazen edge]

too lazy to do the fingers math, i give u the formula and what u need to substitute

$\binom{n+r-1}{r} = \frac{(n+r-1)!}{r!(n-1)!}$

[frosty relic]

Ralepsi

[brazen edge]

where n is the number of different types of blocks, and r is the number of blocks in the tower.

[hollow chasm]

that's not the answer

[brazen edge]

there have fun solving

yes, this is a combinations by with repitition problem

[hollow chasm]

it gives number of different sorted towers, they don;t all have different heights

[brazen edge]

heres a hint: 286 ways of choosing 10 blocks

[hollow chasm]

your way is wrong

[brazen edge]

prove it

[hollow chasm]

you can make different towers with the same height

your way counts different towers

so it's useless

465 is also wrong so you're both wrong

however, i'm correct

it says 94

different problems often have different answers

[brazen edge]

the minimum possible height for the tower is obtained by choosing all blocks of height 2, which gives a height of 2×10=20. the maximum possible height for the tower is obtained by choosing all blocks of height 9, which gives a height of 9×10=90. the range of possible heights for the tower is from 20 to 90.

the formula is wrong

is this even the topic anymore

ok

i forgot

which forum again

man i forgot

ohh

ill do it in the head again wait

can u zoom to the problem

is blurry af

zoom to the problem

bcoz its blurry for me

ok so i expanded it again, yes we didnt needto bcoz the equations are identical because the right hand of the equation is just rearrangement of the terms on the left hand side. when i expanded it, the terms cancel out, leaving me x^n - y^n which is equal to the left hand side of that equation

back to the original problem, let dp[i][j] be the number of ways to build a tower of height j using i blocks. The base case is dp[0][0] = 1, since there is one way to build a tower of height 0 using 0 blocks. for each block, we can choose its height to be either 2, 3, 7, or 9 units. so, for each i from 1 to 10 and for each j from 2 to 90, we have dp[i][j] = dp[i-1][j-2] + dp[i-1][j-3] + dp[i-1][j-7] + dp[i-1][j-9]

[mint ledge]

10C4

umm

pnc?

combinations

[coral kernel]

10000000010000010010000010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010010000010000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

each 1 denotes a height that is valid, first 1 is 94*19, then it decreases by 1 per number

there is definitely a pattern

I also got 465

94 bricks, 4, 10, 19

[mint ledge]

is the answer 210?

[coral kernel]

i can compute any generalized version of this problem if u want

ya

sure

#include <bits/stdc++.h>
using namespace std;

const int TOTAL_BRICKS = 94;
const vector<int> BRICKS = {4, 10, 19};
const int MAX_BRICK_VAL = 19;
constexpr int MAX_TOTAL_BRICK_VAL = MAX_BRICK_VAL*TOTAL_BRICKS+1;

int main() {
  vector<bitset<MAX_TOTAL_BRICK_VAL>> dp (TOTAL_BRICKS+1, bitset<MAX_TOTAL_BRICK_VAL>(0));
  dp[0] = bitset<MAX_TOTAL_BRICK_VAL> (1);

  for (int i = 1; i <= TOTAL_BRICKS; i++) {
    for (int j = 0; j < BRICKS.size(); j++) {
      dp[i] |= dp[i-1] << BRICKS[j];
    }
  }

  int cnt = 0;
  for (int i = 0; i < MAX_TOTAL_BRICK_VAL; i++) {
    if (dp[TOTAL_BRICKS][i]) cnt++;
  }


  cout << cnt << endl;
  cout << dp[TOTAL_BRICKS] << endl;
}```

this is c++

need a compiler ig?

[mint ledge]

hmm

its less than 210 then right?

[coral kernel]

yea just change the const values

should be simple to use

[mint ledge]

@brazen edge

[mint ledge]

.

its less than 210 then right?

icic

[coral kernel]

what are yall computing lol

[mint ledge]

so there must be ones which are repeating

can u paste the question again?

[coral kernel]

i'm getting 68 with your original question

Is there a good solution without just brute forcing it with programming lol

I feel like the aime question might've had a nice solution, i don't think the general question does though