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”.
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 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.
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.
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
In chess a knight may move 2 up/down and one sideways, or 2 sideways followed by one up/down. See the following illustration:
How many knights can you put on a normal 8×8 chessboard so that no knight may take another knight? And can you show that that is the maximum?
This problem was posted at the Dutch mathematics olympiad 1996.
You can check your solution here
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.
Imagine a right triangle (formerly called a rectangled triangle). One side adjacent to the right angle is twice as long as the other. You will not find it very difficult to construct a square from 4 of these triangles.
But is it possible to construct a square from 5 of these triangles? And from 6? From 7?
These problems are derived from ‘doordenkertje’ 12 in the November 1969 issue of ‘Pythagoras’, a Dutch magazine in recreational mathematics. You will need some elementary geometry knowledge to solve this problem.
You can check your solution here
Here are some arrows, all different, and all labelled.
What should be the label of the arrow in the center?
You can check your solution here
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