Ron Barnette's Zeno's Coffeehouse Challenge #56 Result

This challenge prompted a number of correct replies. Over 150 submissions were received and appreciated! I have listed below the original Challenge, followed by two winning examples. I want to thank ALL respondents for their thoughtful time taken with Zeno's Coffeehouse, and to encourage your continued support, as critical thinking exercises are explored for mental growth and recreation.

Thanks!...Ron Barnette

Patterns and Discovery

Charles and Maggie have been discussing patterns lately, especially since nobody offered up a solution to their last Zeno's Coffeehouse Challenge! They were amazed at this, as they dread a possible pattern of inactivity at the Coffeehouse. Alas! So Maggie thought of a three puzzle patterns which will serve as the current challenge, as patrons are invited to detect the patterns and discover the solutions. Both Charles and Maggie hope that this challenge will generate some activity. Please help them out!:)

1. Which symbol is missing in the empty space below?

2. In the following sequence of integers, identify the pattern and list the correct five integers that follow:

3,3,5,4,4,3,5,5,4,3,6,6,8,8.....

3. In the following sequence of letters, identify the pattern and list the correct four letters that follow:

N,E,T,N,X,E....

Submission from Mark Young, who goes on to offer his own challenge. Thanks, Mark! Any Zeno's patrons want to take up Mark's offer?:)

city: Wolfville

state: NS

There is no significance to the 6x6 grid -- we simply read left-to-right from the top right.  Using the numbering scheme 1 = diamond, 2 = club, 3 = square, 4 = inverted club, 5 = heart, 6 = spade, 7 = inverted heart, and 8 = inverted spade, the sequence goes:

1; 1, 2; 1, 2, 3; 1, 2, 3, 4; 1, 2, 3, 4, 5; 1, 2, 3, 4, 5, 6; 1, 2, 3, 4, 5, 6, 7; 1, 2, 3, (4), 5, 6, 7, 8.

The missing value is the one in parentheses.

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Question 2: ..., 7, 7, 9, 9, 8, 6, ...

The Nth element of the sequence (starting at 1) is the number of letters in the English name for N.

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Question 3: R, E, O, E

They are the final letters of the English names of the numbers from 10 down to 1.

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Your turn:  what are the next four values in this sequence:

3, 7, 12, 14, 16, 19, 21, 25, ...

..mark young

Submission from Phil Wilson. Thanks, Phil!!

url: philwilson.wikispaces.com

city: Tokyo

country: Japan

comments: A1: Rotated club. There are eight symbols; the symbols for the four suits, and a rotation of each. A diamond is placed in the first of 36 squares. Counting from left to right, top to bottom, the next diamond is placed in the next square, i.e. one square away, or with no empty squares between. The next diamond is placed two squares away, the next three, and so on. Returning to the top, the next symbol (a club) is placed in the first empty square. The next club is placed one square away (i.e. the second club is one further from the first club than the second diamond was from the first), the third two squares away, and so on. Repeat with the other symbols.

A2: 7,7,9,9,8 The sequence is of the number of letters in the (English) words one, two, three, and so on.

A3: R, E, O, E The letters are the last letters (in English) of the numbers from 10 to 1 (descending order).