# 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

# Knights on a chessboard

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