1) Number square*
Find the missing number:
solution: Here)
Category Archives: Mathematics
What comes next?
What number comes next in the following sequence?
56789
51317
548
…
You can check your solution here
The coffee stain, the archeologist and the reverend
1) The coffee stain
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When I visited an old friend of mine, with his laptop out of order, he had just completed a simple multiplication with pencil and paper. Unfortunately, I spilled some coffee over it. Can you pelase help him to complete the multiplication again?
2) The missing digits puzzle
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In his “Cyclopedia of 5000 Puzzles, tricks and conumdrums” American puzzle master Sam Loyd presented the following puzzle:
Sam Loyd tells a long story about Mormon rock, and in his reprint Martin Gardner skipps this part. I will not follow his example in order to preserve the history, but I do not want to offend anyone, and one should take notice that Sam Loyd was also a master in inventing stories, as can be illustrated with the example on the Swiss flag. Don’t take anything he tells seriously.
Once again discussion has been revived concerning the meaning of the hieroglyphic numbers engraved on Mormon Rock. Mormonism originated only so far back as 1830, so if these weather beaten figures have anything to do with the Latter Day Saints there should be thousands of persons qualified to tell all about them, unless, as some claim, they pertain to the hidden mysteries.
The Mormons migrated in 1838 From Kirtland, O., to Nauvoo, the “City of Beauty” in Illinois and to Salt Lake in 1848. When they left Nauvoo they boasted that their line of march would be twenty four miles long, and was te be headed by a printing press to issue the daily orders of the prophet. It was stated that they were divided up into numerous companies, each one headed by one of the prophet’s wives, and the mysterious fiugures on the Mormon Rock were supposed to give the number of pilgrims in each division.
The figures look like a sum in division engraved upon a sandstone rock. Most of the numbers are illegible, but as some are sharp and clear it is to be assumed that the others were erased maliciously or for a purpose. It is now claimed that either through accident or design the eight legible numbers furnish a key to the mystery, and that the whole is a sum in long division which tells just how many pilgrims marched with each division, and incidentally gave a clue to the number of the prophet’s patrimonial ventures.
It is a remarkable coincidence that the remaining numbers furnish a cluse which easily solves a most interesting historical puzzle, for if you write down the sum in long division, mixing stars with the legible figures as shown, you should speedily be able to guess the numbers which have been erased so that the sum will prove. It reaaly looks as if there should be scores of correct answers, and yet so far as I am aware, but one satisfactory restoration of the missing numbers has been suggested.
Just in case the illustration is not clear, here is a more abstract image of the problem:
3) Dudeney
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In his “536 problems” British puzzle master Henry Dudeney presents the following problem:
He tells it was send to him by the reverend E.F.O. It is, he tells, the first example he has seen of one of those missing-figures puzzles.
You can find these and other puzzles like these in the second edition of my e-book with numbers puzzles.
Sojuko
A Sojuko can be considered as part of the Sudoku family in the sense that the 3×3 square contains each of the digits 1 to 9 exactly once. Some of the digits have been omitted, and the puzzle is to restore the missing digits. As clues four circles are given, holding the sum of the numbers in the squares around them. The solutipon techniques however are reminiscent of Kakuro.
Sojuko number 1
Sojuko number 2
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I found them in “Terdege”, a puzzle add-on of the newspaper “Reformatorisch dagblad”.
Old year – New Year
It is always hard to come up with original puzzles, let alone with a puzzle that has to do with Christmas or new year. Any way: best wishes for 2015 to all of you!
Let’s have a simple problem from the orient. Did you notice that medieval sultans always seem to have an ample supply of beautiful daughters? And that they invariably have strange ways to choose their son-in-law?
This one is no exception. His kingdom had an extensive seashore, and he said to four young men interested in the hand of his daughter: Along the coastline I own many fishing boats. But there is something very peculiar with the number of fishing boats:
when the number is divided by 2, the remainder is 1,
when the number is divided by 3, the remainder is 2,
when the number is divided by 4, the remainder is 3,
when the number is divided by 6, the remainder is 5,
when the number is divided by 7, the remainder is 6
when the number is divided by 8, the remainder is 7
when the number is divided by 12, the remainder is 11
when the number is divided by 14, the remainder is 13
when the number is divided by 18, the remainder is 17
when the number is divided by 21, the remainder is 20
when the number is divided by 24, the remainder is 23
when the number is divided by 28, the remainder is 27
when the number is divided by 32, the remainder is 31
How many fishing boats are there in my kingdom?
You can check your solution here
Billy and the christmas party
Billy desparately wanted to go to the christmas party in the neighbouring village. All the pretty girls from all over the neighbourhood would be there and would be giving kisses to anyone under the mistletoe. And he sure would be there right under the mistletoe as often as he could!
Because he was late, he decided to take a shortcut through the old railway tunnel. It was a straight tunnel and he had an excellent view. When he was still 32 meters from the middle of the tunnel, he heard a train coming up from behind. It was still as far away from the entrance of the tunnel, as the tunnel was long. He immediately ran back and made it with just a meter to spare!
If he had ran to the exit ahead of him with the same speed, the train would have caught him 20 meters before the exit of the tunnel.
Somehow the train driver must not have seen him, maybe by the darkness in the tunnel, as it drove on at the same constant speed all the time.
How long is the tunnel?
What the trains speed was? Oh well, I’m sure little Billy told me, but you know, old age and memory and such – I have completely forgotten. Certainly you are so good you can do without?
Formal disclaimer: Never use an old railway tunnel. There are two possibilities: either the railtrack is in use or it is not. If the track is in use, you may be caught by a scheduled or an extra unscheduled train by surprise. If the track is no longer in use, the tunnel is not maintained and may be be liable to cave in.
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.
61 equals 28?
Make the equation in the picture above correct. To do so, you may freely move the digits around. You may not add other stuff such as plus signs, multiplication signs, and so on.
Recently I purchased “Logic Brain Teasers”, published by Mensa. There was a puzzle on the back cover and while attempting to solve it as a family during dinner, the idea for this puzzle was born.
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.
I do offer my apologies that the puzzle above does not carry a christmas theme, as I had intended. I had two puzzles in mind, but in one I made an error in my calculation and for the other I had insufficient infomation on its origin.
Christmas time is something special in many parts of the world. For some, these are happy days with the family. For others, it’s just a few days off. For me, as an orthodox christian, it is a time of celebration.
Celebration, because where we humans develop irritation, dislike and even hate, God has come to offer a possibility of peace.
Celebration, becuase where we suffer poverty, He has come to share his richness with us.
Celebration, because where we suffer bondage, He has come to set us free.
Celebration, because the God, who is greater than our imagination can comprehend, chose to be born as a small and vulnerable baby.
I wish that you may enjoy the Christmas days and may experience a little bit of the peace, freedom, and richness he wishes to give us.
135
You never realized it. Even though I never met, I’m pretty sure of it. You never realized the number 135 is very special. That is because 1 + 3^2 + 5^3 = 135.
The question is: which three other three-digit numbers have this property?
You can check your solution here
How many numbers with a 5?
Two watches
I started two watches at the same time and found that one went two minutes an hour too slow and the other one minute an hour too fast, so that when I looked at them again the faster one was exactly one hour ahead. Can you figure out from from the picture at what time before noon the watches must have started?
This problem was first posted by American puzzle genius Sam Loyd. It was incorporated into his Cyclopedia of Puzzles on page 30.
You can check your solution here
You are welcome to remark on the quirks in the puzzle, and i especially welcome your solution times. The solutions itself will be published after one week.
justpuzzles 