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100 Year old hat rack puzzle

Topic closed. 1 reply. Last post 5 years ago by RJOh.

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Coin Toss's avatar - shape barbed.jpg
Zeta Reticuli Star System
United States
Member #30470
January 17, 2006
10354 Posts
Posted: June 12, 2011, 1:48 pm - IP Logged

From puzzle master Will shortz

This Hat Rack Puzzle by Sam Lloyd was published 100 years ago in Woman's Home Companion: A hat room contains a wall with 49 pegs, arranged in a 7-by-7 square. The hat clerk has 20 hats that are to be hung on 20 different pegs. How many lines, containing four hats in a straight line, is it possible to produce? A line can go in any direction: horizontally, vertically or obliquely. To explain your answer, number the pegs in order, from 1 in the upper left corner to 49 in the lower right corner; list which pegs you put the 20 hats on, and give the total number of lines containing four hats in a row.


I'm just wondering if this could be modified and applied to lotto, to a playslip somehow.

Those who run the lotteries love it when players look for consistency in something that's designed not to have any.


There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

    RJOh's avatar - chipmunk
    United States
    Member #9
    March 24, 2001
    19831 Posts
    Posted: June 12, 2011, 9:03 pm - IP Logged

    I'm just wondering if this could be modified and applied to lotto, to a playslip somehow.

    Ohio's Classic Lotto(6/49) playslip has a 10x5 grid with the spot for the 50 blank.  I suppose you could use a 7x7 grid to pick/layout your numbers and then tranfer them to the regular play slip.

     * you don't need to buy more tickets, just buy a winning ticket * 
                 Evil Looking