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Can anyone solve AMERICA÷ASIA?

No no no, it's America DIVIDED by Asia, as in Asia colonizes America and divides it into 100 mini countries, not math.
Is that the right answer?

No no no, it's America DIVIDED by Asia, as in Asia colonizes America and divides it into 100 mini countries, not math. Is that the right answer?

The result is a ratio, because of the division sign.
A÷B= attribute(A) / attribute(B)
If you convert the ratio to percentage and use population, than the population of the United States is about 7.1% of the population of Asia. You could add landmass or anything in the logic formula.

The result is a ratio, because of the division sign. A÷B= attribute(A) / attribute(B) If you convert the ratio to percentage and use population, than the population of the United States is about 7.1% of the population of Asia. You could add landmass or anything in the logic formula.
<Comment deleted by user>

Must result in a Chappal with a Burger ln top.

Must result in a Chappal with a Burger ln top.

"solution to this puzzle is 1001"

  • No. ASIA * 1001 = ASIAASIA.
    However, 1011 could work.
"solution to this puzzle is 1001" * No. ASIA * 1001 = ASIAASIA. However, 1011 could work.

Sigh.

Multiple horseys or neigh, America / Asia likely yields a wee fraction, no matter how we evaluate it.

(Futhermore, the ratio is almost continuously changing, as things grow or even contract, moment by moment; so precise evaluation seems to be wishful thinking).

Oh, wait! I must take back the inevitably "wee" part! One such fraction might NOT be wee, after all!

AI informs me -- which doesn't necessarily convince me, mind you -- that the ratio of McDonald's restaurants in America to the number of such restaurants in Asia is approximately 7 / 5 !

That's not wee at all! That's nearly a glass and a half, hopefully of my favorite cold beverage! Which, if I must disclose it, is goat's milk. Although there is a close second.

But check for yourself about the restaurant ratio -- AI sometimes seems to me to be somewhat whimsical. Even if saying so will invite the response: "pot, meet kettle!"

By the way, I will not consider the answer to be 7 / 4 because Lichess has many polyglots, and we need not, and perhaps should not, confine ourselves to English-centric solutions.

Sigh. Multiple horseys or neigh, America / Asia likely yields a wee fraction, no matter how we evaluate it. (Futhermore, the ratio is almost continuously changing, as things grow or even contract, moment by moment; so precise evaluation seems to be wishful thinking). Oh, wait! I must take back the inevitably "wee" part! One such fraction might NOT be wee, after all! AI informs me -- which doesn't necessarily convince me, mind you -- that the ratio of McDonald's restaurants in America to the number of such restaurants in Asia is approximately 7 / 5 ! That's not wee at all! That's nearly a glass and a half, hopefully of my favorite cold beverage! Which, if I must disclose it, is goat's milk. Although there is a close second. But check for yourself about the restaurant ratio -- AI sometimes seems to me to be somewhat whimsical. Even if saying so will invite the response: "pot, meet kettle!" By the way, I will not consider the answer to be 7 / 4 because Lichess has many polyglots, and we need not, and perhaps should not, confine ourselves to English-centric solutions.

@FrogStorm said ^

This is a classic verbal arithmetic (cryptarithmetic) puzzl

I'm not even going to pretend this is me
The explanation you quoted is not a valid solution to a cryptarithmetic puzzle.

Here are the main problems:

The claim that the quotient is 1001 is unsupported.
In a cryptarithm, every letter must correspond to a unique digit, and the equation must hold numerically. Simply arguing from the word structure ("ASIA" and "AMERICA") does not prove that

ASIA
AMERICA

=1001.

Multiplying by 1001 doesn't produce the required word.
If

AMERICA=1001×ASIA,

then

1001×(1000A+100S+10I+A)=1001000A+100100S+10010I+1001A.

Carrying out the arithmetic does not naturally produce a seven-digit number whose digits spell A M E R I C A with a consistent one-to-one letter-to-digit assignment.

The long-division argument is incorrect.
Statements such as

"ASIA goes into AMER exactly 1 time..."
are not mathematically justified. In cryptarithms, you cannot compare symbolic numbers that way without already knowing the digit assignments.

No digit assignment is provided.
A valid solution must specify digits for

A,S,I,M,E,R,C

(all distinct, with A

=0 and M

=0) and verify that

AMERICA÷ASIA=X.

The quoted explanation never does this.

So the proposed answer of 1001 is not a proof and, in fact, is not a valid solution to the cryptarithm.

If this puzzle is intended as a genuine alphametic, the correct approach is to perform a constraint search over the digit assignments. There are seven distinct letters, so there are 10P7=604,800 possible assignments before applying arithmetic constraints, which is very manageable by computer.

@FrogStorm said [^](/forum/redirect/post/HdDKVGgo) > This is a classic verbal arithmetic (cryptarithmetic) puzzl I'm not even going to pretend this is me The explanation you quoted is not a valid solution to a cryptarithmetic puzzle. Here are the main problems: The claim that the quotient is 1001 is unsupported. In a cryptarithm, every letter must correspond to a unique digit, and the equation must hold numerically. Simply arguing from the word structure ("ASIA" and "AMERICA") does not prove that ASIA AMERICA =1001. Multiplying by 1001 doesn't produce the required word. If AMERICA=1001×ASIA, then 1001×(1000A+100S+10I+A)=1001000A+100100S+10010I+1001A. Carrying out the arithmetic does not naturally produce a seven-digit number whose digits spell A M E R I C A with a consistent one-to-one letter-to-digit assignment. The long-division argument is incorrect. Statements such as "ASIA goes into AMER exactly 1 time..." are not mathematically justified. In cryptarithms, you cannot compare symbolic numbers that way without already knowing the digit assignments. No digit assignment is provided. A valid solution must specify digits for A,S,I,M,E,R,C (all distinct, with A  =0 and M  =0) and verify that AMERICA÷ASIA=X. The quoted explanation never does this. So the proposed answer of 1001 is not a proof and, in fact, is not a valid solution to the cryptarithm. If this puzzle is intended as a genuine alphametic, the correct approach is to perform a constraint search over the digit assignments. There are seven distinct letters, so there are 10P7=604,800 possible assignments before applying arithmetic constraints, which is very manageable by computer.

Yes. If the puzzle is interpreted as an alphametic division, where each letter represents a unique digit, then:

Each different letter = a different digit.
Leading letters (A in both words) cannot be 0.
The equation is:
ASIA
AMERICA

=?

Written numerically:

1000A+100S+10I+A
1000000A+100000M+10000E+1000R+100I+10C+A

There are 8 distinct letters:

A, M, E, R, I, C, S

(Actually 7 distinct letters: A, M, E, R, I, C, S.)

This is a constraint satisfaction problem. There are many possible digit assignments to test, but there is no obvious arithmetic solution by hand. It generally requires a computer search over the possible assignments.

If this came from a puzzle book or contest, there is usually an extra condition, such as:

the quotient must also be an integer (or a word),
no leading zeros,
or a specified number of digits in the quotient.

Without those additional conditions, the problem is under-specified.

Leading to non-specified question = non-specified answer

(Note: It's written by myself and not an AI)

Yes. If the puzzle is interpreted as an alphametic division, where each letter represents a unique digit, then: Each different letter = a different digit. Leading letters (A in both words) cannot be 0. The equation is: ASIA AMERICA =? Written numerically: 1000A+100S+10I+A 1000000A+100000M+10000E+1000R+100I+10C+A There are 8 distinct letters: A, M, E, R, I, C, S (Actually 7 distinct letters: A, M, E, R, I, C, S.) This is a constraint satisfaction problem. There are many possible digit assignments to test, but there is no obvious arithmetic solution by hand. It generally requires a computer search over the possible assignments. If this came from a puzzle book or contest, there is usually an extra condition, such as: the quotient must also be an integer (or a word), no leading zeros, or a specified number of digits in the quotient. Without those additional conditions, the problem is under-specified. Leading to non-specified question = non-specified answer (Note: It's written by myself and not an AI)