# Γρίφοι

A Seemingly Impossible Car Riddle. A car travels 75 miles per hour (mph) downhill, 60 mph on flat roads, and 50 mph uphill.

It takes 3 hours to go from town A to B, and it takes 3 hours and 30 minutes for return journey by the same route. Did you solve it? Getting coins out of the bank. Earlier today I set you the following problem.

It was a tricky one, and judging from the BTL comments the solution is eagerly awaited. Let me restate the problem before we get there. It concerns a game on a grid with an infinite number of rows and columns, and starts with three coins in the top left corner of the grid, as illustrated here. The game has one move. Le Monde puzzle [#1087] Can You Solve An Oxford Interview Question? The Sliding Ladder Problem.

Oxford ranks as one of the world’s best universities, and part of the admissions process is an interview to test an applicant’s ability to think.

This problem is paraphrased from a sample interview question in Mathematics. A ladder is placed vertically on a wall. What shape does the midpoint of the ladder trace as the ladder slides against the wall to the floor? What if the ladder instead fell backwards to the ground by rotating from its base—what shape would the midpoint of the ladder trace then? What’s The Average Distance Of Two Points On A Circle? You may have seen my video about picking two points randomly on a square which Cleve Moler, inventor of MATLAB, wrote an excellent article about it.

Today’s problem is a similar problem for the circle. On a circle with a radius of 1, pick two random points on the circumference. What is the average distance between the two points? Can You Solve The Train Length Puzzle? Thanks to Pedro for suggesting this problem!

Every day, a train passes a train station along a straight line track, and the train moves at a constant speed. Two friends, A and B, want to determine how long the train is. Lacking proper equipment, they devise the following method. Μαθη...μαγικα: Μεταπρόβλημα Μουντιάλ. The Circle Inscribed In A Parabola Calculus Puzzle – Can You Solve It? I thank Chad Facciolo for sending me this puzzle!

A circle with radius 1 is tangent to two points of the parabola y = x2. What is the area bounded between the inscribed circle and the parabola, as shown in the diagram? Can you figure it out? Watch the video for a solution. Can You Solve A Math Word Problem That Stumps US College Students? A Working Together Problem – Mind Your Decisions. Simon Tatham's Portable Puzzle Collection. Introduction This page contains a collection of small computer programs which implement one-player puzzle games.

All of them run natively on Unix (GTK), on Windows, and on Mac OS X. They can also be played on the web, as Java or Javascript applets. Can you solve it? The whisky puzzle that will have you on the rocks. Hello guzzlers.

If you are now abstaining from alcohol, as many end-of-year over-indulgers do, today’s puzzle is for you. Here’s a full whisky bottle. Can You Solve The Horse Grazing Area? Sunday Puzzle – Mind Your Decisions. A horse is tied to an outside corner of a 20 foot by 10 foot rectangular barn.

What is the maximum area the horse can graze outside, if the rope has length L? Solve for L = 5 feet and L = 25 feet, and find the exact answer. If you are up for a challenge, solve for L = 50 feet. You can solve for the answer to 3 decimal places. Can You Solve The Diluted Wine Puzzle? Famous 16th Century Math Problem – Mind Your Decisions. A servant has a method to steal wine.

He removes 3 cups from a barrel of wine and replaces it with 3 cups of water. The next day he wants more wine, so he does the same thing: he removes 3 cups from the same barrel (now with diluted wine) and replaces it with 3 cups of water. The following day he repeats this one more time, so he has drawn 3 times from the same barrel and has poured back 9 cups of water. At this point the barrel is 50% wine and 50% water. Tanya Khovanova's Math Blog » Blog Archive » Who Is Left? Centaurs, manticores, and minotaurs roam their planet. Their society is very democratic: any two animals can become sex partners. When two different species mate, their orgasm is so potent that they merge into one creature of the third species. For example, once one centaur and one manticore make love, they are reborn as one minotaur. At the beginning of the year 2016 there were 2016 centaurs, 2017 manticores, and 2018 minotaurs. They mated non-stop and at the end of the year only one creature was left on the planet.

This is one of those puzzles that I love-hate. The Day After Tomorrow Is Yesterday Riddle – Mind Your Decisions. This problem is popular on Facebook and social media. “When the day after tomorrow is yesterday, then today will be as far from Wednesday as today was from Wednesday when the day before yesterday was tomorrow. What day is today?” Can you figure it out? Watch the video for a solution.

Μαθη...μαγικα: Καλοκαιρινό πρόβλημα νικητήριας στρατηγικής.... The Rectangle Ratio, A Surprising Answer – Sunday Puzzle – Mind Your Decisions. Start with a square with length 1; label it R1. Create a new rectangle as follows: attach a rectangle of area 1 to the right side and then attach a rectangle of area 1 to the top side. The border of this shape is a new rectangle, R2. Starting with R2, we can attach another pair of rectangles of area 1 to form a new rectangle, R3.

## The Riddler

Math Arguments: 515: Pascal Proof. The Friendship Theorem – Sunday Puzzle – Mind Your Decisions. In a group of 6 people, you might find that some people are friends with each other on Facebook, or you might find that no one is friends with each other on Facebook. There are many combinations for how people can be friends or not. Show that there is always a group of 3 people in which either: –All 3 people are mutual friends on Facebook. Spies Sharing Secrets – Sunday Puzzle – Mind Your Decisions.

On a successful mission, each spy obtains a secret piece of information. The n spies need to share all their secrets with each other, which they accomplish through a series of phone calls between 2 spies at a time. During a call, a spy can share all the secrets the spy knows, including secrets learned from previous calls. What is the minimum number of phone calls needed so every spy learns all of the secrets? Διασκεδαστικά Μαθηματικά: Το κυνήγι της πάπιας. An integer programming riddle. Avoiding The Troll – Sunday Puzzle – Mind Your Decisions.

## Θεωρία αριθμών

Οι Βρύσες. Scribd. Σπαζοκεφαλιές και μαθηματικοί γρίφοι απο το ιστολόγιο μαθη..μαγικα (h… Nick's Mathematical Puzzles: Solution 90. Does there exist an integral power of 2 such that it is possible to rearrange the digits giving another power of 2? Numbers are written in standard decimal notation, with no leading zeroes. We argue by reductio ad absurdum. Suppose the digits of 2a can be rearranged to give 2b, where a < b.

Consider 2b − 2a. Mikesmathpage. Art of Problem Solving. About Careers Contact Log In / Join School Store Community Resources.

## Logic Puzzles

\$2015\$ νομίσματα. Πάνω σε ένα τραπέζι βρίσκονται απλωμένα νομίσματα. Κάποια είναι γυρισμένα ώστε να δείχνουν κεφάλι και κάποια δείχνουν γράμματα. άνθρωποι δικαιούνται να κάνουν το εξής: O 1ος θα γυρίσει ένα οποιοδήποτε νόμισμα. Ο 2ος θα γυρίσει οποιαδήποτε νομίσματα, ... ο -ιοστός θα γυρίσει οποιαδήποτε νομίσματα..., ο 2015ος θα γυρίσει όλα τα νομίσματα. Tετραγωνικοί άσσοι.

Μαθηματικά δυτικά του Πέκος. Οι Ψεύτες. Γρίφοι - Προβλήματα. Το Κιβώτιο. Ο δάσκαλος. Kangaroo. Le Monde. Ακέραια Μπισκοτάκια. Κλόουν. \$θ,2θ,3θ,...,Νθ\$ Εξίσωση (10) Η μέρα των Χριστουγέννων και ένα πρόβλημα του μαθηματικού διαγωνισμού Putnam !! Φέτος τα Χριστούγεννα πέφτουν Κυριακή. Πέρυσι ήταν Σάββατο , εν γένει η μέρα των Χριστουγέννων αλλάζει κάθε χρόνο. Ένα χριστουγεννιάτικο πρόβλημα μερικής απασχόλησης !! Πέντε φίλοι και ο πίθηκος. Δύο αδέλφια. ▪ Πέντε μηδενικά. Προβληματάκι...

## Γεωμετρία

Ευκλείδεια Γεωμετρία (Α Γενικού Λυκείου - Γενικής Παιδείας): Ηλεκτρονικό Βιβλίο. Η «Ευκλείδεια Γεωμετρία» έχει ένα διττό ρόλο να εκπληρώσει: να μυηθεί ο μαθητής στη συλλογιστική την οποία εκφράζει το αξεπέραστο λογικό-επαγωγικό σύστημα του Ευκλείδη και να ανταποκριθεί στις σύγχρονες εκπαιδευτικές επιταγές. Το βιβλίο αυτό, σύμφωνο με τα πλαίσια συγγραφής που έθεσε το Παιδαγωγικό Ινστιτούτο, ευελπιστεί ότι θα οδηγήσει τους μαθητές του Λυκείου να γνωρίσουν την αυστηρή αλλά και λιτή μαθηματική γλώσσα, ελπίζοντας ότι θα συνεισφέρει στη μαθηματική παιδεία του τόπου, αναπτύσσοντας το ρεαλισμό της μαθηματικής λογικής και σκέψης.

Το έργο αυτό είναι αποτέλεσμα της συλλογικής προσπάθειας μιας ομάδας μαθηματικών, οι οποίοι αποδεχόμενοι την πρόσκληση του Α.Σ. της Ελληνικής Μαθηματικής Εταιρείας εργάστηκαν συστηματικά για την πραγματοποίησή του. Θα θέλαμε να ευχαριστήσουμε θερμά: το Δ.Σ. της Ελληνικής Μαθηματικής Εταιρείας για τη βοήθεια που μας πρόσφερε σε όλη τη διάρκεια της συγγραφής του έργου, τον Καθηγητή του Ε.Μ.Πολυτεχνείου κ. Euclid's Elements, Introduction. Euclid’s Elements form one of the most beautiful and influential works of science in the history of humankind. ▪ Τρία κλάσματα.

## Συνδυαστική/Πιθανότητες

Rubik cube. Another Singapore Birthday Math Problem Stumps The Internet. This is not about the famous Cheryl’s birthday problem. According to Mothership, a Singapore math question on students’ birthday months has everyone stumped. Again.