Spot the differences

Once a month, or once every other month, I try to take a more in depth look at a puzzle type. This month I want to have a look at the “spot the differences” puzzles. This is a pretty popular type of puzzle, Bing turns up at least 4 different websites and the google playstore has at least 10 apps. URLs of the websites are mentioned at the end of this article. The trigger for this post is my recent acquisition of a magazine “zoek de verschillen” (find the differences) by Denksport, the largest puzzle publisher in the Netherlands.

1) Spot the differences

Try to find all 15 differences!
(The picture has been taken in the Netherlands, in the tourist town of Vaals).

You can check your solutions here

While making this puzzle, trying my hand at some of the puzzles in the magazine, and browsing around on the web, I noticed there are several types of changes:
1 – an object appears in one image and not in the other. An example is a traffic sign that has an arrow in one image and no arrow in the other. The object often is small.
2 – the object is present in both images, but with different colors. For instance, if you have a dish with colorful sweets, one of the sweets has been changed from green to orange.
3 – the object is present in both images, but in one image it is longer, shorter, wider or narrower than in the other. In one of the puzzles in the web, I noticed a garbage can, attached to a pole, reached to the pavement on the left imgae while in the right image it was a foot above the pavement.
4 – the object is present in both images, and the object is identical in both images, but in a different spot. For example, that crow on the roof is sitting near one end of the roof or in the middle.

What makes a puzzle tough? Which differences are hard to spot? I could not find any scientific research on this topic. Generally, I’d say that small differences are harder to spot than big differences. But some differences seem to be ignored by the eye or mind, even though they are not particularly small. A change in a background is often harder to spot than one in the foreground. Changes to the top of an object seem to be spotted more easily than changes to the bottom.

2 identicals
A second format that the afore mentioned magazine applies is that of 6 copies, and you have to find the 2 identical copies.

The abundant availability of digital photos has greatly enhanced the possibility for everyone, both amateur and professional, to create these puzzles. I don’t have photoshop, but MS paint served me well during the creation of the puzzles above. Before the age of electronic manipulation, the images were often handdrawn. You can find one on the english language wikipedia.

You can check your solutions here

3) Subdivisions
A large photo is subidivided into small rectangles, with rows and column labelled. A few of the rectangles are copied below the photo and the puzzler has to find out which small rectangle they correspond with.

What are the coordinates of the two cut outs?

You can check your solutions here

4) Cutout
A rectangle is cut out from a photo and displayed below it. Several other sections are copied below the photo, and the puzzler has to find out which is the cut out which fits into the picture. The cut outs are tilted, and I currently lack the skills or tools to do this for you.

5) Links
Here are some of the links I found and which work:
* http://www.spotthedifference.com/ : spot 4 differences in a couple of images, allowing you to give up and try again later. Differences are both small and large
* http://spot-the-differences.com/: 5 differences, all well visible, timed.
* http://www.coolmath-games.com/0-spotthedifference2: timed, retry option. Alas flash seems required.
*

Crosswords – but don’t worry.

Don’t worry, this blog is not turning into a crosswords puzzle blog, and neither is it changing into a word puzzl;e blog.

But every now and then there is a nice variation on a traditional theme, and for programmers there is a nice variation using regexp here

In an upcoming post I intend to go into depth on numerical crossword variations,

For now: Have fun!

The lazy comrade

Yesterday, that is, the day before I wrote this, I received the English translation of Boris Kordemsky’s “Russian Puzzles” (Matematicheskaia smekalka, which translates as ‘Math savvy’), edited by Martin Gardner. It was first published in 1956. In the first few chapters it contains many old chestnuts, sometimes disguised in a new coat. Though I am not a big fan of Martin Gardner, he did preserve the Russian atmosphere well. Many of the familiar puzzles can also be found in the works of Henry Dudeney and Sam Loyd. Alas Martin Gardner left out a series of problems towards the end related to number theory (‘too difficult for the american public’). Now that that sounds like two insults :).

It inspired me to make a small variation:
“I will plough this field at an average of 200 furrows a day,” Pjotr told his comrades in the Kolkhoz. And indeed he started out right away the next day. He set off relaxed; making just 100 furrows a day on the first 1/3 of the field , but he could blame some initial problems for thet. Once the initial problems were solved, he was able to plough at a speed of 200 furrows a day for the middle 1/3 of the field.
He realized that he was still lagging behind on his promise and made some small improvements, enabling him to complete the final third of the field at 300 furrows a day. At the next meeting of the kolkhoz he told with satisfaction that he had lived up to his promise. The party administrator however denied his claim:
“Tovarisj Pjotr,” he said, “I think you err.”

Who was right?

You can check your solutions here

A new puzzle is posted every Friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.

Matchsticks 11

Add one matchstick to make an even number. No matchstick may bay be moved.

You can check your solutions here

In these days matchsticks are increasingly harder to come by for a variety of reasons. Of course it is very good that the number of smokers is falling. Those who still yield to this unhealthy habit seem to prefer other ways to light their cigarettes. Other forms of smoking tobacco such as cigars and pipes have also decreased dramatically, at least in my personal surroundings.
In the home matchsticks were mainly used to light the fire for cooking. The introduction of electric cooking has made them largely superfluous.

Luckily, matchstick puzzles can also be made with other materials such as toothpicks and nails (not the ones on your finger, but the ones you beat into wood). There are a fair number of matchstick puzzles on the web, and here is a small selection:

• http://matchstickpuzzles.blogspot.nl/ – my personal favorite, with over 300 of them, and devoted solely to matchstick puzzles. Also the most extensive one, and contains more puzzles than some of my matchstick puzzle books


• http://blog.aimsedu.org/category/puzzle/toothpick-puzzles/ – an excellent overview with lots of historical info. A mix of logic and math problems, and as far as i know the first to call them toothpick puzzles.


• http://www.puzzles.com/PuzzlePlayground/Matches.htm a nice collection

A happy 2016!

First of all I wish each and everyone of you a happy and healthy 2016!

Having said that, can you tell me what the last two digits are of 2016^2015?

You can check your solution here

2015 in review

The WordPress.com stats helper monkeys prepared a 2015 annual report for this blog.

Here's an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 43,000 times in 2015. If it were a concert at Sydney Opera House, it would take about 16 sold-out performances for that many people to see it.

Click here to see the complete report.

Christmas 2015 – a doublet

Charles Lutwige Dodgson, alias Lewis Carroll, did not just write Alice in Wonderland, but also books on Mathematical subjects and puzzle books. The story goes that Queen Victoria, who reigned Britain during Charles live, was so enchanted by ‘Alice in Wonderland’, that she wrote the author and asked him to send her a copy of his next book. Charles dutifully did sent her his next book – on a mathematical subject.

Charles was also the inventor of a type of puzzle where one word has to be changed into another word by changing one letter at a time.
Example:
cat
cot (replace ‘a’ with ‘o’)
cog (replace ‘t’ with ‘g’)
dog (replace ‘c’ with ‘d’)
Lewis Carroll says that he invented the game on Christmas day in 1877. The first mention of the game in Carroll’s diary was on March 12, 1878, which he originally called “Word-links”, and described as a two-player game. Carroll published a series of word ladder puzzles and solutions, which he called “Doublets”, in the magazine Vanity Fair, beginning with the March 29, 1879 issue. Later that year it was made into a book, published by Macmillan and Co.The one which Charles originally used was the problem to change HEAD into TAIL:
HEAD
heal (Replace ‘d’ of ‘head’ to ‘l’)
teal (Replace ‘h’ of ‘heal’ to ‘t’)
tell (Replace ‘a’ of ‘teal’ to ‘l’)
tall (Replace ‘e’ of ‘tell’ to ‘l’)
TAIL (Replace ‘l’ of ‘tall’ to ‘i’)
The puzzles have been called Doublets, Word-links, Laddergrams, Word-golf, and Word-ladders.

At this time of the year, a Christmas puzzle seems appropriate. Over the past century, attention at Christmas seems to have shifted from Mary and her Baby to the christmas tree.

Try to change the word MARY into TREE in the fewest number of steps. Or, if you prefer that, you can change the word TREE back to MARY.

Marcel Danesi, Ph.D., on Psychologytoday.com, believes that ‘solving them will give the verbal areas of the brain a veritable workout. The reason I believe this to be the case is that a solution entails knowledge of both word structure and semantics. The main semantic process involved is word association and, thus, recall, which is a powerful form of brain-activating thinking, at least as I read the relevant research. We are of course faced with the usual problem of trying to understand or explain how the research translates into benefits through puzzle-solving. The way I look at it is that puzzles such as the doublet can only be beneficial to overall brain health. As one’s semantic memory begins to wane through the aging process, giving the semantic parts of the brain a puzzle workout can only be advantageous‘

You can check your solution here

You are welcome to remark on the puzzle: its wording, style, level of difficulty. I love to read your solution times. Please do not spoil the fun for others by listing the solution. Solutions will be posted after one or more weeks.

Sources and further reading:
http://www.psychologytoday.com/blog/brain-workout/200908/the-doublet-puzzle-masterpiece-the-pen-lewis-carroll
http://books.google.nl/books?id=JkQCAAAAQAAJ&dq=charles+dodgson&pg=PP1&redir_esc=y#v=onepage&q&f=false
https://en.wikipedia.org/wiki/Levenshtein_distance The Levehsteind distance between two words is the number of operations that is needed to change one word into another by adding a letter, removing a letter or replacing a letter.
https://en.wikipedia.org/wiki/Damerau%E2%80%93Levenshtein_distance The Damerau–Levenshtein distance is identical, but also allows the transpostion of two adjacent characters.
The distance between two words in a doublet as used by Dodgson is a special case of the Levenshtein distance: inseryion and deletion are not allowed, while all intermediate words must appear in a dictionairy.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4269387/ doublets as a complex network

Bongard problem (5)

The Russian scientist M.M. Bongard published a book in 1967 that contains 100 problems. Each problem consists of 12 small boxes: six boxes on the left and six on the right. Each of the six boxes on the left conform to a certain rule. Each and every box on the right contradicts this rule. Your task, of course, is to figure out the rule.

You can check your solutions here

You can find more Bongard problems at Harry Foundalis site, and I intend to publish more problems in the future.

A new puzzle is posted every friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.

Droodles

Did you ever notice that people often draw all kinds of figures during meetings? Here are some coded, abstract droodles.

There is a hint

The 4 cards (Cont’d)

The brainteaser of the 4 cards is a nice teaser, which made me wonder if it could be generalized. Indeed I found a couple of ways to vary upon this theme.

1) The 3 values
There are six cards in front of you. Each of them has a letter on one side and a number on the other side. Three of them have letters face up: A, B and C. The other three have numbers face up: 1, 2 and 3.
How many cards (and which) do you want to check if you want to know every card with ‘C’ on the front face has a ‘2’ on the reverse?

You can check your solutions here

2) The three triangular blocks
Another way to vary on this subject is to have more than one backside. Consider the wooden blocks depicted in this figure. They have three sides (plus a top and a bottom). One side has a letter, one side a color and one side a number. Only one side is facing you. You can only rotate them clockwise. You are not allowed to get up and walk around them.
As you can see, each block now has two ‘backsides’, a leftback and a rightback. The letter is either A or B, the number either 1 or 2, and the colour either orange or purple.



As you can see there is an ‘A’, a ‘2’ and an ‘Orange’ facing you.

How many rotations do you have to make to ascertain if the rightback of all B is purple?

You can check your solutions here