Billy’s Big Christmas Party

Billy was delighted to have gained entry to the Big Christmas Party in the neighbouring village. There were stalls and booths littered throughout the hall.

1) The apple pie stall^**/*****
The first stall he walked to showed delicious steaming hot pieces of apple pie on display. Several other kids had gathered in front of it.
A sign read:
4 and 7 give 33
3 and 2 give 5
8 and 5 give 39
A middle aged lady behind the stall held up two numbers: 6 and 3.
“This woman must be the wife of the math teacher,” he whispered to his neighbour.
The lady must have overheard him, because she laughed:
“Young man, I am the math teacher.”
But she was quickly satisfied when Billy quickly figured out the correct answer, collected his piece of apple pie and walked to the second stall.

You can check your solution here

2) The hot chestnuts stall^****/*****
The second stall displayed dishes of chestnuts filled with had chestnuts. A man was roasting the chestnuts on a small coal fire and serving them with several sauces.
A sign displayed some calculations:
11 + 11 = 8
12 + 59 = 18
18 + 47 = 16
23 + 39 = 16
He held up two numbers for the children in front of his table: 22 and 45.
Slightly softer than the previous time, Billy whispered to the girl besides him:
“Do they have two math teachers here?”
The girl looked at him saying:
“Did you ask if we have two math teachers here?”
The man heard it and laughed: “No, I’m the Arts teacher.”
Billy quickly grasped the problem and found the sum of 22 and 45.

You can check your solution here

3) The mince pies^****/*****
The third stall displayed a lovely looking plate with mince pies.
A piece of cardboard listed:
5 and 6 give 6
3 nd 7 give 7
7 and 8 give 8
She held up two cards showing 4 and 12. “What number do they give?” she asked. “I’ll tell you in advance the answer is not 12.”
To prevent him from asking, the girl besides him told him:
“No, she doesnt teach math. She teaches English.”

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.

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.