16

The answer is Explanation: Here's a picture with all the numbers:


15

Looks like So the number is


12

In the second subtraction, the number being subtracted is three digits, and the first digit isn't 1. So it must be at least 200, and the divisor is at least 21. Since the first digit of the divisor isn't 2, the divisor must be at least 30. In the first subtraction, the number being subtracted is at least twice the divisor, but is only two digits. So the ...


9

The answer is Explanation:


9

Kind of cheating, but... 1,736 | ( 1736) x 5,843 | ( 5843) ----------- | _,___ | ( 5208) __,___ | ( 69440) _,___,___ | ( 1388800) + _,___,___ | ( 8680000) ----------- | __,___,___ | (10143448) Answers the question in its literal form. ;-) Also, note that with lots of zeroes in the multiplicands this works: ...


8

You are looking for least percentage, without concerning with the Difficulty of the puzzle. In that case, the percentage can be made arbitrarily small. Here is an example with 31 digits removed: 999)*********(******* *** *** *** *** *** 0 Here the format AAA)BBB(CCC means AAA is dividing BBB to get the ...


7

Start at the number 1. You should now be able to find how to fill in the missing value.


7

Since this does not have the no-computers tag I have used a computer to I did it in a relatively similar way to a manual approach The Python code: Running that code (sub-second):


6

I think I found the answer. Step one to find the divisor. I started with Now this number start making sense in my mind. Here's how Second step of division. Third step of division. Fourth/Final step of division Here is my actual work Answer


5

Answer Explanation First I will replace the $X$'s with different lowercase letters, so its easier to refer to them. F a 8 b c +---------------- A d C | e f B D g h i j k m J ------- G n g h o p H ------- q r i j s t u E ------- The ...


5

Answer: Reasoning: . . . . EDIT: Formatting


4

The "useless digits" of hints 3 and 4 are The columns are really labelled The missing digits are The rows are I confess I'm not sure I understand hint 1; perhaps it's


4

Solution: Dividing the puzzle up into sections: Some reasoning (more to come when I'm back home with a scanner): Assuming no leading zeroes: The rest is trivial-ish:


3

Edit: Changed the reasoning based on Jaap Scherphuis's comment as it seems more natural. I think the answer is Reasoning Examples


3

First Answer : Second Answer may be :


3

Doorknob's _,___ | ( 1000) x _,___ | ( 1000) ----------- _,___,___ | (1000000) ----------- 1,___,___ | (1000000) is not uniquely solvable; how about e.g. 1,234 x 1,000 ----------- 1,234,000 ----------- 1,234,000 On the other hand, isn't the following uniquely solvable? _,___ x _,___ ---------- _,___ +_,___,...


2

I ran a computer program and I was wondering why it didn't find a solution. It's because some numbers presented as 4-digit number are in fact 3-digit numbers. So I ran it again and it found 2350 solutions! 20 solutions have XXBDXXXX mod AXC = 0. (The problem didn't say it had to be 0) Here's all 20 solutions with mod 0: 124 * 80800 = 10019200 (A,B,C,D,E,F,...


2

I believe the answer is


2

Since: Then: So the number is:


2

I get Because


1

It's probably a typo Given that there are only 2 examples to work with, it must be a very simple formula. Usually the formula uses each number once. I wrote a computer search for all ways to combine the 4 numbers around the circle with operations +, -, *, / in a way that it produces the value in the circle for the left and right case. The only formulas ...


1

After @SteveV's progress: Then, given the language tag, we now Giving Meaning (approximately)


1

Ok so this has puzzled me for a while. I have a partial answer based on some assumptions. This test is designed for primary school children, looking at the rest of the paper everything is basic so this puzzle should be the same. I think we are supposed to ignore the bottom horizontal line and instead picture the shape in 8 equal slices. I think the two ...


1

partial answer


1

Here’s a pretty MathJax rendering of the solution (which I found independently after slimeArmy’s answer was posted). $$ % Define a very small, pale comma: \newcommand{\c}{\hskip{-0.5pt}\large\color{#888},\huge\hskip{-6.5pt}} % If you want to eliminate the commas, just do % \newcommand{\c}{} % % Define a red "5": \newcommand{\5}{\color{#D11}5} % Change the ...


1

In More Mathematical Puzzles and Diversions, ch. 14, Nine More Problems, problem 5, Martin Gardner gives the problem of reconstructing the following long division: xx8xx xxx)xxxxxxxx xxx --- xxxx xxx ---- xxxx xxxx ---- Gardner credits the problem to P. L. Chessin of the Westinghouse Electric ...


1

In a $4 \times 4 $ multiply there are $ 8 $ single digit multiplies and $ 7 $ column additions. In the sense of simultaneous equations, you would expect to be able to delete $ 15 $ digits and find your way home. The fact that you know where digits belong, as well as pattern in arithmetic (like a product $5$ must come from $5$ times odd) gives you further ...


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