It’s a long time ago we had a matchstick puzzle. THis is a variant of what my old friend Biep posed me.
Make the following equation correct by moving just 1 matchstick:
Difficulty: ****/*****
New puzzles are published occasionally on the first Friday of the month. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.
It’s a while ago we had matchstick puzzles, so here’s one again. And yes, you are perfectly right, matches are on the way out with electric cooking and all such. Luckily, you can use nails or toothpick sticks instead. I mentioned it in a previous post and I’m now also mentioning it in the title of the post.
In the image below you see 18 matchsticks aka nails aka toothpicks making up six squares. Now re-arrange the 18 matchsticks to make twenty.
New puzzles are published at least twice a month on Fridays. You can check your solution here.
Before Nov 6 we didn’t have a match stick puzzle for quite a while, so let’s have one again.
1) How many rectangles are there in this square?**/*****
2) How many rectangles are there in an mxn rectangle?**/*****
The previous puzzle can be generalized from 3×3 to any size, an m x n rectangle. How many rectangles are there in an mxn rectangle?
New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. The difficulty of puzzles is rated on a scale of 1 to 5 stars. You can check your solutions here.
It’s a while ago since we had matchstick puzzles. And the last series we had, were with numbers 0-9 as found on digital watches.
This puzzle is a bit different. You see
4 (or 6) parallelograms*/*****
Move to matches to make 3 squares
New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solutions here.
For the past couple of months, I have been publishing puzzles with playing cards. Henry Dudeney was British formost puzzle master of the late 19th / early 20th century. In this series his puzzles, as published in “Amusement in mathematics”, may not be omitted.
1) The card frame puzzle***/*****
In the illustration we have a frame constructed from the ten playing cards, ace to ten of diamonds. The children who made it wanted the pips on all four sides to add up alike, but they failed in their attempt and gave it up as impossible. It will be seen that the pips in the top row, the bottom row, and the left-hand side all add up 14, but the right-hand side sums to 23. Now, what they were trying to do is quite possible. Can you rearrange the ten cards in the same formation so that all four sides shall add up alike? Of course they need not add up 14, but any number you choose to select.
You can check your solution here
2) The cross of cards***/*****
In this case we use only nine cards—the ace to nine of diamonds. The puzzle is to arrange them in the form of a cross, exactly in the way shown in the illustration, so that the pips in the vertical bar and in the horizontal bar add up alike. In the example given it will be found that both directions add up 23. What I want to know is, how many different ways are there of rearranging the cards in order to bring about this result? It will be seen that, without affecting the solution, we may exchange the 5 with the 6, the 5 with the 7, the 8 with the 3, and so on. Also we may make the horizontal and the vertical bars change places. But such obvious manipulations as these are not to be regarded as different solutions. They are all mere variations of one fundamental solution. Now, how many of these fundamentally different solutions are there? The pips need not, of course, always add up 23.
You can check your solution here
3) The “T” card puzzle***/*****
An entertaining little puzzle with cards is to take the nine cards of a suit, from ace to nine inclusive, and arrange them in the form of the letter “T,” as shown in the illustration, so that the pips in the horizontal line shall count the same as those in the column. In the example given they add up twenty-three both ways. Now, it is quite easy to get a single correct arrangement. The puzzle is to discover in just how many different ways it may be done. Though the number is high, the solution is not really difficult if we attack the puzzle in the right manner. The reverse way obtained by reflecting the illustration in a mirror we will not count as different, but all other changes in the relative positions of the cards will here count. How many different ways are there?
You can check your solution here
4) Card triangles***/*****
Here you pick out the nine cards, ace to nine of diamonds, and arrange them in the form of a triangle, exactly as shown in the illustration, so that the pips add up the same on the three sides. In the example given it will be seen that they sum to 20 on each side, but the particular number is of no importance so long as it is the same on all three sides. The puzzle Pg 116is to find out in just how many different ways this can be done.
If you simply turn the cards round so that one of the other two sides is nearest to you this will not count as different, for the order will be the same. Also, if you make the 4, 9, 5 change places with the 7, 3, 8, and at the same time exchange the 1 and the 6, it will not be different. But if you only change the 1 and the 6 it will be different, because the order round the triangle is not the same. This explanation will prevent any doubt arising as to the conditions.
You can check your solution here
1) A 5×5 grid***/*****
Which of the 5 cards on the right should take the place of the card turned down?
You can check your solution here
New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.
We had two previous posts on dice problems, which you can find here and here.
This is the third post in a small series on dice puzzles. The first one was about the polar bear puzzle and its variations, the second one posed some alternate patterns.
In this post I want to explore some dice puzzles by the British grand master of puzzles, Henry Dudeney.
1) The dice numbers.
I have a set of four dice, not marked with spots in the ordinary way, but with Arabic figures, as shown in the illustration. Each die, of course, bears the numbers 1 to 6. When put together they will form a good many, different numbers. As represented they make the number 1246. Now, if I make all the different four-figure numbers that are possible with these dice (never putting the same figure more than once in any number), what will they all add up to? You are allowed to turn the 6 upside down, so as to represent a 9. I do not ask, or expect, the reader to go to all the labour of writing out the full list of numbers and then adding them up. Life is not long enough for such wasted energy. Can you get at the answer in any other way?
This puzzles was published as puzzle 96 in “Amusement in Mathematics”
You can check your solutions here
2) A trick with dice
The first problem I want to have a look at was published by British puzzler Henry Dudeney in his book “Amusement in Mathematics” (and before that probably in one of the magazines in which he had a monthly column).
I ask you to throw three dice without me seeing them. Then I tell you to multiply the points of the first die by 2 and add 5. Multiply the result by 5 and add the point of the second die. Multiply the result by 10 and add the points on the third die. Mention me the result and I will immediately tell you the points on your three dice.
For example, if you throw 1, 3 and 6, the result will be 386, from which I could at once say what you had thrown. How do I do that?
This puzzles was published as puzzle 386 in “Amusement in Mathematics”
You can check your solutions here
3) The Montenegrin dice game
It is said that the inhabitants of Montenegro have a little dice game that is both ingenious and well worth investigation. The two players first select two different pairs of odd numbers (always higher than 3) and then alternately toss three dice. Whichever first throws the dice so that they add up to one of his selected numbers wins. If they are both successful in two successive throws it is a draw and they try again. For example, one player may select 7 and 15 and the other 5 and 13. Then if the first player throws so that the three dice add up 7 or 15 he wins, unless the second man gets either 5 or 13 on his throw.
The puzzle is to discover which two pairs of numbers should be selected in order to give both players an exactly even chance.
You can check your solutions here
This is the third post with puzzles about playing cards.
1) Which hands are valid?****/*****
In a game, the following six hands are valid plays:
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Which of the following three hands is / are valid?
You can check your solution here
New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.
Last month I published two puzzles with playing cards. Here are two more in the same line:
For those who missed the puzzles, look at the figure below. It shows 16 cards, one of which is hidden. At the bottom you find 4 cards. Which of those 4 cards should replace the hidden card?
3) Playing cards puzzle 3***/*****
You can check your solution here
4) Playing cards puzzle 4***/*****
You can check your solution here
New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.
While waiting for my appointment with the dentist I thumbed through the magazines, looking for good puzzles. I had little hope of finding any more than a crossword or sudoku, but to my surprise I encountered a new format in the magazine plusonline. The magazine does have a website, as the name suggests, but I couldn’t find the puzzles there.
In all puzzles the problem is: which of the four cards at the bottom should replace the blue card?
Here are two puzzles in the same vein. I did make a small change: the original puzzle had rows of three cards, which I changed into cards rows of four cards.
1) Playing cards square nr 1***/*****
You can check your solution here
2) Playing cards square nr 2***/*****
You can check your solution here
New puzzles are published at least twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars.
Be prepared for more puzzles of this type in a few weeks.
justpuzzles 