# Origami Manifold Puzzles

The September issue of the Dutch magazine Quest came with a small origami puzzle booklet. It contains 8 puzzles. The puzzle in each case is to fold a square piece of paper, such as depicted below, in such a way that one side is black and the other side is white.

There is a book published by “The Incredible Company“. You can freely download a free pdf with 5 puzzles from there site. The book does not seem to mention an author, though I suspect the author is Jérôme Morin-Drouin. Play testers were two people named Caro and Felix.

To solve the puzzles below, print them, cut them and fold them such that the result is a sqiuare, white on one side and black on the other.

Puzzle 1*/*****

Puzzle 2*/*****

Puzzle 3*/*****

No solutions will be given.
Credits go to Quest for pointing out this puzzle type, to the incredible company for coming up with the idea and to my daughter Margreet for puzzle number 2 above. NUmbers 1 and 3 are my own work.

# Cryptarithm – weapons

Cryptarithm*
In the following cryptarithm, replace every letter with a digit. The same letter always represents the same digit and identical digits have always been replaced by the same letter:

A new puzzle is published every Friday. 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 three stars.

You can check your solutions here

New puzzles are published at least twice a month on Friday. 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 three stars.

# How many?

1) The logicians club**/*****
Yesterday I visited a club of logicians. It’s a very special club, only trained logicians are admitted as members. During the club meetings, all members are required to speak the truth the entire evening, or to lie the entire evening. All members were seated around the circular table, truth tellers and liars alternating. I was not a member and watched from a distance. The president of the club welcomed all the members, and especially me as a guest.
He also explained some more rules which I admit I have quite forgotten. One part of the evening consisted of questions the members asked about the rules, while another topic were the finances.
At the end of the meeting, I asked the president how many members this club had. He happily told me that all 20 members had been present. When I was about to leave, I suddenly realized that the president himself need be trusted, and asked the secretary if the president had spoken the truth.
“Oh no!” the secretary exclaimed. “You should not believe the president, tonight he was a notorious liar! At this evening’s meeting, all 21 members were present!”

Whom should I believe? And why?

The puzzle above comes from “Denken als Spiel”, by Ernst Hochkeppel, one of the earliest puzzle books I obtained.

You can check your solutions here

2) The party***/*****
Once there was a party where everybody with 100 people. Everybody shook hands with a number (some or all) of other people. Everybody present was either a liar (someone who always lies) or a Truthteller (someone who always speaks the truth).
When leaving the party, everybody was asked with how many Truthtellers he or she had shaken hands with. All answers 0, 1, 2, etc till 99 occurred exactly once.

How many Truthtellers were at the party?
This puzzle can also be watched as a video by Mindyourdecisions on youtube.

You can check your solutions here

New puzzles are published at least twice a month on Friday. 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 three stars.