Questions tagged [calculation-puzzle]

A puzzle that involves numerical calculations, such as multiplication and addition.

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7
votes
3answers
973 views

A small pandigital equation

_ _ _ _ _ × 8 = _ _ _ _ _ There is a number that you can put in the left-hand side of the above equation so that the blanks are filled in using every digit from ...
13
votes
2answers
1k views

Directions on an infinite compass rose

An old sailor, by the name of John, was in his attic with his bright young great-nephew Stewart, showing him all the old tools they used to use while at sea. Stewart was fascinated by all the ...
4
votes
3answers
1k views

Crack the Code #4

The park bench has been compromised as a safe location, so you decide to meet in the lobby of the nearest hotel. Again, the envelopes are traded securely, along with the money you are receiving for ...
5
votes
3answers
935 views

Crack the Code #3

You return to the bench after cracking the last code, and you notice an envelope on the ground directly under it. You put down your envelope with the previous code and pick up the new one, ...
7
votes
4answers
2k views

Crack the Code #2

After the last bank encounter, you decide that you could make a living off of just cracking codes (as if robbing banks wasn't enough). A shady man meets you on a park bench and slides you an envelope, ...
35
votes
1answer
4k views

Ernie's automatic parking valet

I was helping Ernie out in his shed a while back, when his favorite screwdriver suddenly wore out. I offered to go and pick up a new one for him and Ernie thought it was a great opportunity to test-...
7
votes
6answers
2k views

Crack the Code #1

You are a bank robber, and you come across a safe. It has a combination lock of 4 digits. Careful research (and stealing papers at the bank) has given you multiple clues as to the code - just barely ...
1
vote
1answer
561 views

How do I count Hamiltonian paths of grid?

Let's say there is a 5x5 grid with a starting position in the upper left corner, and an ending position is lower left corner. How do I count how many Hamiltonian paths there are through the grid? I ...
6
votes
1answer
990 views

Puzzle of Random Numbers

My friend sent me his puzzle: it's S2LQEQnXk4DP+WsyP1aURD+lz4JSteeOPz3tO7Yiu1dv5fFCr31uegHUpVGqyXk7WjX95TDALus8Gj6nnoGHwj0MLE2AfpB2KTQEIxVvGMyun2XLb+PTcqzVAoFQLr48 ...
11
votes
5answers
2k views

Sorting cards using max 3 stacks

You have a stack of N cards numbered from 1 to N in random order. You want to sort the cards in ascending order using the following procedure: Your initial stack is stack 1. You distribute the cards ...
8
votes
1answer
794 views

A different extension of the sum and product puzzle

How far down the rabbit hole of not knowing can we go? While working on the generalization of I don't know the two numbers... but now I do, I thought of these two extensions. Both have the same ...
6
votes
1answer
2k views

Generalization of Sum and Product puzzle

I heard from a clever person that for the problem mentioned before: I don't know the two numbers... but now I do a solution exists even if we change 100 to infinity. So the formulation would be ...
3
votes
2answers
3k views

Men digging holes

Suppose 9 men take 9 hours to dig 9 holes in the ground. (a) How many hours would it take 3 men to dig 3 holes? (b) How many men would it take to dig 54 holes in 54 hours?
7
votes
4answers
625 views

Paint the rectangle with least movement

There is a painting brush tool that can paint a circle area of $1$ unit radius. What is the shortest paint track for painting at least a $100*100$ units rectangle area on wall? How much did the brush ...
-3
votes
1answer
2k views

Number of days to fill the Lake with 1/32th part

There is a lake in which every day some new lotus flowers grow. Their growth follows a pattern; if on a given day there are X flowers, then on the next day there will be 2X flowers will be there. So ...
4
votes
3answers
545 views

Flowers For a Patient

A woman wanted to visit her friend at the hospital. She had walked 500 meters from her front door before remembering that she wanted to pick up some flowers. She went back to the florist she had ...
2
votes
4answers
10k views

clock values using just “9” (and some operators)

Sometimes a clock is posted on Facebook and the likes where digits are substituted by mathematical expressions. A friend of mine asked me what is the smallest numbers of "nine" which let one express ...
6
votes
2answers
2k views

Find the age of the ship and of the boiler

Some years back I was travelling by a cargo ship from New Zealand to Tahiti. I was curious to look around the ship one day and in the boiler room I asked a man how old the ship was. He smiled and ...
1
vote
3answers
460 views

Balance the Equation

Peter found an old piece of paper that an equation was written on it. Some of digits or operations are unreadable. Help Peter to complete the balanced equation. The equation is: $87+?3?12-4?2=?36-15??...
15
votes
2answers
786 views

Santa Claus flies to the South Pole

It is a little known fact that Santa Claus is in fact a vampire. Why else would he spend so much time near the North Pole and travel only at night? Yes, he fears daylight! His problem is that ...
3
votes
2answers
2k views

A modified version of apples and oranges logic

Question: You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. ...
9
votes
2answers
1k views

Integer grid problem

I found this programming related problem too difficult for me. The problem asks to find 16 integers and form a 4x4 grid $$\left(\begin{array}{cccc} n_1 & n_2 & n_3 & n_4 \\ n_5 & n_6 &...
-1
votes
1answer
483 views

Products of three primes that bound RSA numbers [closed]

Let $N$ be some number. Let $R$ and $S$ be semiprimes (ie, each is a product of two prime numbers) such that $R \le N \le S$. For quite a few numbers $N$ we can find $R, S$ such that $S-R$ is small;...
7
votes
1answer
560 views

A cube puzzle (Multiple of 6)

If you have a cube, say, $3 \times 3 \times 3$, you know that mathematically it's made of $27$ ($3*3*3$) smaller cubes. Now, just remove one full line of smaller cubes (in this case, 3 smaller cubes). ...
3
votes
2answers
514 views

Find a high-scoring 53-digit prime number chain

Let a “number chain” be a series of numbers, $n_0, n_1, ... n_{m-1}$ for some $m$, such that in base 10 the low digits of $n_i$ match high digits of $n_{(i+1)mod m}$. For example, after the number ...
2
votes
1answer
395 views

Make a wide tower of bridge-shapes

In this question, bridge stands for the illustrated convex quadrilateral, constructed from three equilateral triangles. Letters A, B, C, D, E are assigned to each unit length of periphery as shown in ...
7
votes
8answers
3k views

Divide 3 cakes into 4 equal parts?

You have three cakes of diameter 20cm, 16cm and 12cm respectively as shown in the figure. They all have the same height. Now your task is to divide these 3 cakes into 4 equal parts and you are ...
1
vote
2answers
389 views

Bottle rinsing with fixed amount of wash water

Given $L$ units of wash water, we want to wash out a vessel (eg, a milk bottle, honey jar, chemistry flask...) using a series of rinses that minimize the amount of Stuff other than water remaining in ...
5
votes
5answers
3k views

A Set of Water Jug Challenges

You've probably heard about challenges with water jugs, so why not try a few? Use 3- and 5- liter jugs to get 4 liters. Use 5- and 7- liter jugs to get 4 liters. This one's different. How many ...
5
votes
3answers
2k views

A Sand Timer Challenge

Which (if any) of these intervals is it possible to measure given two sand timers (which change from question to question)? There are no minute marks, halfway points, etc. A. 7 minutes with 4- and 5-...
3
votes
2answers
495 views

Your age and my age [closed]

This is not a very difficult problem, but it seems that it hasn't been asked here. It's one of my favorites, so here we go: I am twice as old as you were when I was as old as you are. When you ...
6
votes
3answers
505 views

Magic back yards

My back yard forms a rectangular grid of squares except some of the squares are missing as they are covered by pipes or a small tree. The layout is as follows. A 'x' indicates a square that is free ...
0
votes
3answers
42k views

Candle timing measurement [duplicate]

You are given two candles of equal size, which can burn 1 hour each. You have to measure 90 minutes with these candles. (There is no scale or clock). You are also given a lighter.
7
votes
4answers
370k views

Puzzle of putting numbers 1-9 in 3x3 Grid to add up to 15

In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15. I have only been able to come up with one solution: $$\begin{array}{ccc} 6 &...
4
votes
2answers
568 views

What's the largest number that can be obtained in the process of solving a numbers game on Countdown?

Countdown is a British game show in which people try and make the longest possible word out of nine given letters, reach a target number using six given numbers and basic arithmetic, and then solve a ...
4
votes
1answer
1k views

Is there a general strategy for decoding Brainfuck mutations?

There are many Brainfuck variations used in puzzles in geocaching, for example Ook! They are usually not so hard to decode because they are 'standards' - therefore the substitution is googlable, there ...
-3
votes
1answer
1k views

Can anyone explain me how to solve this problem? [closed]

Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they did half the job. Then they worked together for another 3 hours and they had to do (...
9
votes
3answers
2k views

Stranded Nomad Riddle

Background Story A nomad is injured in the desert. And he can't move, but fortunately an oasis is nearby, and he can stay there for enough time until rescue arrives. But the water is a magical water, ...
6
votes
4answers
2k views

To be a bookworm

I have a complete set of encyclopaedias on my bookshelf, beautifully bound and neatly arranged with volume 1 on the left and volume 32 on the right. They were a talking point when I bought them 30-odd ...
8
votes
10answers
5k views

Find the missing number: A Pentagonal pattern puzzle

This question is based upon the figure shown below. $$ \begin{array}{|ccc|c|ccc|c|ccc|} \; & 41 & \; & \; & \; & 31 & \; & \; & \; & ? & \; \\ 5 & \; ...
7
votes
3answers
1k views

How do I solve the “Between Worlds” Android puzzle game?

I've been struggling for a while with the Between Worlds Android game, and have not yet solved it. I've only noticed a couple vague properties that hold in localized cases. To operate the puzzle, ...
3
votes
1answer
320 views

Is there a more specific name for this type of arithmetic puzzle?

There are arithmetic puzzles with some numbers (typically four) and rules for combining them (perhaps just the four basic arithmetic operators or including things like combining digits 2 and 3 to make ...
5
votes
2answers
1k views

How many digits can be removed from a division puzzle?

Similarly to How many digits can be removed from a multiplication puzzle and still give only one answer? I am curious about division puzzles. I know this puzzle: . It has only 2 out of 42 digits $\...
16
votes
2answers
12k views

Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
13
votes
2answers
3k views

How many distinct unsolvable Rubik's cubes exist?

I wanted to answer this question: Why can't I have only one edge piece flipped on a 3X3 Rubik's cube? by saying that it is homomorphic to the illegal state in this question: Why is a ...
4
votes
1answer
951 views

Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong ...
10
votes
3answers
2k views

The Magic Stick

Here's a relatively easy puzzle that's actually entirely my own creation. An old guru in an Asian monastery is showing his beloved student his gallery of items that he has either collected or kept ...
29
votes
7answers
8k views

Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
5
votes
3answers
978 views

How many digits can be removed from a multiplication puzzle and still give only one answer?

There's a common category of mathematical puzzle which involves determining missing numbers in a long multiplication problem. As an example from this site (problem 10): ...
9
votes
2answers
615 views

What size of puzzle is appropriate?

I am making a puzzle based on a Project Euler problem. Here is the puzzle at present: What path in the triangle below, starting from the top number with each step moving to one adjacent number in ...