Questions tagged [calculation-puzzle]
A puzzle that involves numerical calculations, such as multiplication and addition. Use with the [mathematics] tag.
1,244 questions
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Find all integers n such that the sum of the factorials of its digits equals ⌊√n⌋ [closed]
Find all integers n such that the sum of the factorials of its digits equals ⌊√n⌋.
For example, if n=2025, then 2!+0!+2!+5!=⌊√2025⌋, although this is not true.
How can you find all integers n that ...
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What pattern did Excel see in my data?
I was filling out the rightmost column of this set of cells from top to bottom. (The content of that column is intended to be manually calculated using the numbers to the left plus some hidden weights,...
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When is the next Narcissistic date?
A Narcissistic date is a date such that when all digits of a date is raised to certain nth power and add them all together, the sum is equal to YYYY.
As an example, if we take today's date, which is ...
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Sum of a sequence
The last two days I have dreamt of solving a puzzle to escape hospital, and I just woke up so wanted to jot this down quick.
Imagine a snake with some number of segments. The segments' labels are $(1,\...
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When is the next "Factorion" date?
A "Factorion" date is a date such that when written to either one of M!+M!+D!+D!+Y!+Y!+Y!+Y! (MM/DD/YYYY), D!+D!+M!+M!+Y!+Y!+Y!+Y! (DD/MM/YYYY) , or Y!+Y!+Y!+Y!+M!+M!+D!+D! (YYYY/MM/DD) is ...
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Find a number whose divisors' factorials add up to a given number
This question did never came out in any contest.
If $\sum_{d\mid n} d!=$ ...
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Make numbers 1-40 using only 2, 0, 2, 6
Try to make all numbers 1-40 using the digits 2, 0, 2, 6.
Rules:
Use all four digits exactly once.
Allowed operations: +,−,×,÷,! (factorial), $x^y$ (exponentiation), √ (square root).
Parentheses and ...
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Why does that person have a phobia on these dates?
Note: I created this puzzle.
A person has a phobia on certain dates - January 15 and February 3. While some dates like April 15 and July 24 also appear unlucky, that person is more afraid of those ...
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An old book with an ancient numeral puzzle: How many coconuts?
I came across the following puzzle in "Puzzles, Patterns, and Pastimes from the World of Mathematics" by Charles F. Linn (https://archive.org/details/puzzlespatternsp00linn/ page 50):
For ...
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Pattern of the Chessy Sequence
Find the pattern of the chessy sequence.
Kn1 = 43x73x101x137
Kn2 = 25x41x26161
Kn3 = 43232323
Kn4 = 2x16170607
Kn5 = 32x4801369
Kn6 = 23x32x7x59x1087
Kn7 = 32x4801369
Kn8 = 2x16170607
(All of the ...
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How much am I? - Four-digit number riddle
I came from any distinct four-digit number.
While I was it, I reordered myself, marking my maximum and minimum.
I saw a difference between them, then made that difference myself.
I repeated this until ...
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Find the Hidden Rule!
Handmade Puzzle.
Solve the puzzle, and find the hidden rule. (This is not evil.)
[Notations / Rules]
0. Latin Square - Each rows and columns should have distinct digits from 1~9.
1a. - Maximum cell: ...
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Determine if there exists a future date such that the sum of digits of MM/DD/YYYY is equal to ⌊√yyyy⌋
Note: I created this puzzle.
Determine if there exists a future date such that the sum of digits of MM/DD/YYYY is equal to $\lfloor\sqrt{yyyy}\rfloor$, where MM is the month, DD is the day, and YYYY ...
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2.25³ᐧ³⁷⁵ vs 3.375²ᐧ²⁵
Without using a calculator or a computer can you determine which of these two numbers is bigger: 2.253.375 or 3.3752.25?
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Does this even have unique solution? - Logic Steps Blocked -
Solve this puzzle.(Handmade)
Rules:
Every rows and columns should have unique digits(1~9) once.
Regions(): Yellow-colored cells should not have same digits.
Max(): Bigger than adjacent cells.
Min(): ...
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With given numbers, make the number 87 [closed]
Try to make the number 87 using 5,5,1,0
Rules:
Use all four digits exactly once.
All mathematical operations are allowed.
Concatenations are not allowed.
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This is not about the last century...
1926 $\longrightarrow$ 19
1927 $\longrightarrow$ 16
1928 $\longrightarrow$ 20
1929 $\longrightarrow$ 19
1930 $\longrightarrow$ 19
1931 $\longrightarrow$ 15
1932 $\longrightarrow$ 18
1933 $\...
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Moving water by repeated equilibration
There are 100 full water tanks and 100 empty ones. You are given a hose that can connect any two of them in order to equilibrate the water level between them. All the tanks are cubical in shape, of ...
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How many measures to know the area?
How many measures are required to figure out the area of the annulus below?
(The center of the two circles are equal.)
Attribution to my math lecturer. :)
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Get ready for some multiplication!
As the title says, get ready for some multiplication! The answer is a word.
?? = _ _ _ (divisible by 9)
?? = _ (odd)
?? = _ (divisible by 3)
?? = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
?? = _ _ _ _ _ ...
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Aha! Diamond sum
With a suitable aha! moment, this puzzle can be easily solved in your head without knowing any formulas such as the sum of the first N positive integers.
What is the sum of the numbers in the ...
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Puzzle involving circles around numbers
Source: It is from the book The IQ Testbook by Philip Carter and Ken Russell
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I need Answer Urgently [closed]
Choose the missing term out of the given alternatives:
E4, G9, J25, 049, V121, ?, T289
E169
G169
G225
E225
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All triangles lead to Rome
I am looking for a specific building in Rome, Italy. To find it, follow these steps.
Fill the 12 small triangles in the gray area in the 6 large triangles.
Finish the 6 large triangles in a logical ...
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Make 987654321 = 123456789 by adding as few as operators as possible
This equation is false. Make it true by adding as few operators as possible:
987654321 = 123456789
Only the operators + - ...
user106806
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Two Operand Change
Make this equation true by removing up to two digits/operands* or setting them to custom value/operands:
(55 - 4) × 44 = 55
You can first remove the second 5 in (55-4), then set both 4s to 5s, but ...
user106806
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Add a dot (in a weird way) to make the equation true
Add one dot to make the following equation true.
Everything is in base-10 and the dot can’t change the equal sign.
I first encountered this puzzle many years ago (source unknown) well before I joined ...
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Barely made it!
What should replace the question marks inside the unit circles below? Explain your reasoning.
Note: Ignore the rectangular frame around the numbers. Not part of the puzzle.
Edit: Added the calculation-...
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Mrs. McTavish's Holiday
Taken from "Puzzle Parade" by Morley Adams (Faber 1948)
"It's nice to be in the country," said Mrs. McTavish, "but of course it costs money. First there was the taxi, then the ...
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Partially hidden
If you keep adding more and more forever, time will keep going backwards, but never reach 2:45.
What do the clocks above represent? The answer is an 8-letter word.
Edit: I added an important tag... (...
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Fill a grid to make a Latin square where the 9 regions have the same sum
The instructions are to place the digits 1, 2, 3, 4, 5, 6 in the cells to form a Latin square (no digit appearing twice in a row or column) in which the numbers in each region add to the same sum.
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Fill the circles so that the sum of the three numbers along each of the ten lines is the same.
Using all the numbers 1, 2, 3, ..., 11 (each exactly once), put a number in each circle so that the sum of the three numbers along each of the ten lines is the same.
Attribution: Puzzle by M. Varga ...
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Is the product of square roots of consecutive Fibonacci numbers (starting with 2) ever an integer?
Consider the product:
$ \sqrt{2} \times
\sqrt{3} \times
\sqrt{5} \times
\sqrt{8} \times
\cdots \times
\sqrt{F_n} $
where the integers inside the square roots are the Fibonacci numbers ...
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Can you find sets of 4 (or 5) positive integers such that their pairwise sums give consecutive numbers?
Warmup question:
Is it possible to find four positive integers such that their pairwise sums give six consecutive numbers?
Main question:
Is it possible to find five positive integers such that their ...
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Min-Max Circuit Deduction
Have solved this one? Try this!
Handmade Puzzle: Min Max Circuit
Fit in the numbers satisfying the following rules.
Each row and column should contain 1~9 distinctly.
- Maximum cell: This cell ...
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A binary multiplication cryptarithm. Replace the asterisks with 0 or 1.
Beginner puzzle (suitable for people who are new to puzzle solving).
The only digits in the binary system are 0 and 1.
The operations of addition and multiplication are defined by:
0+0=0, 0+1=1+0=1, 1+...
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Make 101520 with 6 6's
Make the number 101520 with 6 6's.
Rules:
All 6's must be used exactly once
The operations allowed are addition (+), subtraction (-), multiplication ($\times$), division ($\div$), exponents and ...
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Continuing from the Interesting Number Solving Problem - Candidates of the Center Number
Continuing from Will’s interesting problem.
Let a1 + c = b1, a2 + c = b2, …, an + c = bn, and each a1 ~ an, b1 ~ bn, c are distinct number between 1 and 2n+1.
What number can c be?
For Will’s problem (...
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Place 1 through 7 into the circle to make equal sums
The three lines in the figure below divide the circle into seven regions. Can you arrange the numbers 1 to 7 in these regions so that for each of the lines, the sums of the numbers on either side are ...
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SIX / NINE = 2 / 3 alphametic
To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!
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Fix 52 ÷ 5 - 1 = 4
Due to lack of mathematic skills, I wrote myself the following equation but it is wrong:
52 ÷ 5 - 1 = 4
Fix the incorrect equation by moving only one digit.
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A number is product of 45 consecutive integers, find the value of n without a calculator
Note: This question was asked in our school's 2017 Math contest for 15 year old students.
If (n) × (n+1) × (n+2) × ... × (n+44) = ...
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\$‡ + \$» = ¤§‡, ^ × \$ × & = ¤»&, ~ × §¤^ = #~!
$‡ + $» = ¤§‡, ^ × $ × & = ¤»&, ~ × §¤^ = #~!, ^¤‡~$»!&§# = ?
This is a puzzle of my making. I’m not seeking solutions. I simply wished to reach an ...
user104142
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Three-Digit Digit Puzzle
I am a 3 letter word. My hundreds place times two is the tens place. The tens place minus two is the ones place. What number am I?
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Soldier Enrollment
There are 200 soldiers in a camp, and every evening either five or seven of them are on duty. On every odd day, five are on duty, and on every even day, seven are on duty. So, on the first day, five ...
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Multiplication alphametic with stars and moons
This puzzle is from Quantum Quandaries (100 brainteasers from Quantum the magazine of math and science)
Mystery of the stars
The moons in the accompanying number rebus denote one and the same digit. ...
8
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Arithmetic Sudoku
Consider this sudoku puzzle:
All normal sudoku rules apply.
But it has some extra conditions:
A,B,C must form an arithmetic series in that order. Equivalently, A+C=B+B.
D,E,F must form an arithmetic ...
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Place numbers so that the sum of the numbers inside each “Olympic” ring is the same
The five “Olympic rings” cut the plane into 15 pieces (not counting the infinite piece on the outside).
Arrange the numbers 1 to 15 (using each exactly once) in these pieces, one number in each piece,...
4
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1
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366
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Number hides number now…
Find the number hidden by numbers.
18, 41, 147, 176, 256, 98, 90, 65, 11, 256, 242, 40, 34, 225, 256
Hint 1.
Edit - Sorry, but this puzzle is quite dirty. You might not think that this is an answer ...
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4
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1
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What’s the trick here?
My friend brought me 5 cards, and asked me to think about 1 number from 1 to 32.
Then he started to ask: “Is that number in here?”
After he checked all of this 5 cards, he got my number in (less than) ...
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