Iq test if i have two tetrahedral pyramids

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Discussion Overview

The discussion revolves around a problem involving the combination of two tetrahedral pyramids made of golf balls, specifically addressing how many balls are needed to create a larger pyramid when the two smaller pyramids are of different sizes. The conversation includes mathematical reasoning and exploration of tetrahedral numbers.

Discussion Character

  • Exploratory, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant states that combining two equal-sized tetrahedral pyramids requires a minimum of 20 balls to form a larger pyramid.
  • Another participant suggests that the same 20 balls can be used if the pyramids are made of 4 and 10 balls, but this is challenged by others.
  • A participant emphasizes the need to use all balls and notes that there are six remaining in a specific scenario.
  • Concerns are raised about the potential size of the answer, with one participant expressing hope that it will not exceed 1000.
  • Multiple participants express confusion regarding the question and the mathematical formulation, particularly about the integer solutions for the equation derived from the pyramid sizes.
  • There is a discussion about the correct interpretation of tetrahedral numbers and how they relate to the problem, with references to triangular numbers and their sums.
  • One participant corrects themselves regarding the shape being discussed, realizing they were considering an octahedron instead of a tetrahedron.
  • A later reply provides a specific answer of 680 balls, indicating a combination of pyramids of heights 14 and 8 to create a height of 15, but this is presented without consensus on the correctness of the approach.

Areas of Agreement / Disagreement

Participants express differing interpretations of the problem, with no consensus on the correct approach or solution. Confusion about the mathematical formulation and the requirements of the problem persists throughout the discussion.

Contextual Notes

There are unresolved mathematical steps and assumptions regarding the definitions of tetrahedral numbers and their combinations. The discussion reflects uncertainty about the correct interpretation of the problem and the calculations involved.

datatec
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this one i got from an iq test

if i have two tetrahedral pyramids of equal sizes made of golf balls and I combine them (presuming every ball is used) the minumum amount of balls needed would be 20 to make one larger pyramid. What would the minimum be should the two smaller pyramids be different sizes? :wink:
 
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The same 20 balls (you may have 2 pyramids made of 4 and 10 balls).
 
Last edited:
Nope

You need to use all the balls. In your case you have six remaining.
 
I hope that answer is not some giant number, and that there will be a solution within 1000...but I'm having doubts.
 
I don't think I understand the question correctly.
You said if you combine the number of balls from two equally sized tetrahedral pyramids and add 20, then you have the number of balls needed to make a pyramid one size larger.
The number of balls needed for a pyramid of size n is:
[tex]\sum_{i=0}^ni^2=\frac{1}{6}n(n+1)(2n+1)[/tex]
so the equation to solve is:
[tex]2\frac{1}{6}n(n+1)(2n+1)+20=\frac{1}{6}(n+1)(n+2)(2n+2)[/tex]
to find the size of the smaller pyramids.
But it has no integer solutions...

Possibly, my picture of making pyramids with golfballs is wrong.
Stacking them like this will not make them tetrahedral, but I don't see any other way to do it.
 
Galileo said:
I don't think I understand the question correctly.
You said if you combine the number of balls from two equally sized tetrahedral pyramids and add 20, then you have the number of balls needed to make a pyramid one size larger.
The number of balls needed for a pyramid of size n is:
[tex]\sum_{i=0}^ni^2=\frac{1}{6}n(n+1)(2n+1)[/tex]
so the equation to solve is:
[tex]2\frac{1}{6}n(n+1)(2n+1)+20=\frac{1}{6}(n+1)(n+2)(2n+2)[/tex]
to find the size of the smaller pyramids.
But it has no integer solutions...

Possibly, my picture of making pyramids with golfballs is wrong.
Stacking them like this will not make them tetrahedral, but I don't see any other way to do it.

The question is simply, "What 2 dissimilar tetrahdra (built from balls) can be combined to make a new tetrahedron, using exactly the number of balls contained in the smaller ones ?"

The case of 20 balls would be a solution were this question lacking the word 'dissimilar'. It has nothing to do with the current question.

Next, a tetrahedral number of height n, is the sum of the first n triangular numbers, and so, should be given by the sum

[tex]\sum_{i=0}^n{i(i+1)/2}=\frac{1}{12}n(n+1)(2n+1) + \frac {n(n+1)}{4}[/tex]

Triangular numbers are : 1,3,6,10,15,21,28,...
Tetrahedral numbers are : 1,4,10,20,35,56,84,120,...

We are looking for 2 different Tet. Numbers that add to give a third one.
 
Gokul43201 said:
Next, a tetrahedral number of height n, is the sum of the first n triangular numbers, and so, should be given by the sum

Oh yeah... a tetrahedron has 4 sides.
I can' t count. :redface:
 
In white.
751966976
 
Wrong Again

I´m afraid you're wrong.
Clue in white:

The answer is below 1000
 
  • #10
Ahh, i was doing half of an octahedron, not a tetrahedron.

ANSWER :
680 balls, by a height of 14 and a height of 8 TH's to make a height of 15 TH.
 

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