Perfect Practice Makes Perfect

# Holiday Puzzle #21 – Alice in Self-Referential Land

Begin at the beginning and go on till you come the end; then stop.” – Lewis Carroll

Alice returned to wonderland to find that things were very little changed.  She ran into many of her old acquaintances along the way, discovering they too had changed very little.  However, she quickly discovered that her new adventures would have a self-referential twist.

Below are two of Alice’s encounters with the caterpillar.  In the first puzzle, the caterpillar pulls colored and numbered chips from a bag, hiding the numbers from Alice.  He provides Alice (and you) with some details about the numbers and you have to determine what they are.  In the second puzzle, Alice selects numbered cards from a deck which the caterpillar peeks at.  He again provides Alice (and you) with some details about the numbers and you have to determine what the numbers are on each card.  The following puzzles are self-referential – so beware – the numbers may change before your very eyes!

Puzzle 1

The caterpillar held a black bag containing different colored chips. On each chip, there was a number.  From the bag, the caterpillar selected four different color chips:  red, green, blue and yellow.  He looked at the number on each chip and then placed it face down in front of Alice.  Alice saw the color of each of the four chips, but could not see any of the numbers.  The caterpillar noted the following:

The number on the red chip was the number of selected chips with an odd number
The number on the green chip was the number of selected chips with an even number
The number on the blue chip was the number of selected chips with a number greater than 1
The number on the yellow chip was the number of selected chips with a number less than 2

Can you tell the sum of the four numbers on the selected chips?
Can you tell what number was on each chip?

Puzzle 2

Alice selected five cards from a deck of cards and placed them face down in front of the caterpillar. The caterpillar secretly looked at each card. After looking at the fifth card, he smiled and said “very interesting! The cards contain the numbers 1,2,3,4 or 5, either once, more than once or not at all”. He then told Alice the following:

The number on the first card is the number of odd numbers on the selected cards
The number on the second card is sum of the numbers on the first and fifth cards
The number on the third card is a number different than all of the other numbers
The number on the fourth card is the difference of the numbers on the first and fifth cards
The number on the fifth card is the number of even numbers on the selected cards

Can you tell the numbers on each of the selected cards?

I consider these puzzles to be very challenging.  Be patient and go fast slowly.  Here are links to two more self-referetial puzzles #7 (a collection of self-referential puzzles) and #14 (Who Killed Phil M. Mupp).  I am currently generating a book of original self-referential puzzles, all of which have a story behind them (much like the above).  The first chapter is devoted to Alice and her new adventures with self-referential puzzles.  I hope to have the book out early next year.  Click here to look at all of my currently available puzzle books (on Amazon).  Good Luck and pass the puzzles onto others who may enjoy them!