Can You Solve the $$\sqrt {car}=37$$ Puzzle?

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Discussion Overview

The discussion revolves around the puzzle represented by the equation $$\sqrt {car}=37$$. Participants explore the meaning and implications of this equation, suggesting various interpretations and related mathematical relationships.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that there is a specific sense in which $$\sqrt {car}=37$$ can be considered correct, inviting others to explore this meaning.
  • Another participant notes that 37 is a prime number and proposes that if c = 1369, then a and r could be reciprocals of one another under certain conditions.
  • A different participant hints at a broader system by providing additional equations: $$\sqrt {cdo}=38$$, $$\sqrt{cpw}=42$$, and $$\sqrt{doj}=49$$, suggesting that all these square roots must hold true within the same framework.
  • Several participants express attempts to solve the puzzle, with one asking about how to create a "spoiler" for their solution.
  • One participant acknowledges a mistake in their previous post and indicates they will correct it in a separate message.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the solution to the puzzle, with multiple competing interpretations and approaches presented by participants.

Contextual Notes

Participants' contributions include various assumptions about the relationships between the variables in the equations, but these assumptions remain unresolved and depend on the definitions used within the context of the puzzle.

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TL;DR
My daughter discovered this using an unusual program I wrote for her.
There is a precise sense in which it is correct to say: $$\sqrt {car}=37$$

The puzzle is to figure out in what sense this is true.

[What made this so exciting for her is that 37 is her favorite number, and that she was obsessed with car models at the time].
 
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37 is prime.

but we could have c = 1369
and if a NE r, ( ie if a = r = 1 ), then they can be just the reciprocal of one another.

( I would like the large bunny in the corner for my girlfriend. )
 
The solution I'm looking for is much more natural than that. I'll give a big hint: $$\sqrt {cdo}=38$$ and $$\sqrt{cpw}=42$$ All 3 square roots have to be true under the same system. One more, just for fun: $$\sqrt{doj}=49$$
 
Last edited:
Base 26 comes to mind ...
 
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Filip Larsen said:
Base 26 comes to mind ...
Winner!
 
I think I have solved it. How do I create a "spoiler"?
 
Buzz Bloom said:
I think I have solved it. How do I create a "spoiler"?
In edit message window, touch the arrow next to the 3 dots. Spoiler is one of the options.
 
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The three letters "c", "a", and "r" each have a different value between 1 and 26 inclusive.
The notation represents a three digit (base 26) number. That is c has a coefficient of 262, a has a coefficient of 26, and r has a coefficient of 1. This produces the equation below.
676 c + 26 a + r = 372 = 1369​
c = 1 because c>1 implies 676 c > 1369.
Therefore,
26 a + r = 693.​
Now
693/26 = 26.65...​
Therefore, a = 26, and r = 693 - 676 = 17.

The cdo problem is also solved the same way, although c now has a different value.
c = 2, 26 d + o = 382 = 1444 - 1352 = 92
Now
92/26 = 3.5...​
Therefore d = 3 and o = 14.

Oops. I now see that I made a mistake. I will correct it in a separate post.
 
Last edited:
Base on the the cdo solution
c = 2
d = 3
o = 14
in the previous post, I now see that in the car problem
c = 2
a = 1
r = 17.

The general pattern is
each letter has the value of its position in the alphabet - 1.
 
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  • #10
Buzz Bloom said:
Base on the the cdo solution
c = 2
d = 3
o = 14
in the previous post, I now see that in the car problem
c = 2
a = 1
r = 17.

The general pattern is
each letter has the value of its position in the alphabet - 1.
Correct.
 

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