[HN Gopher] A Puzzle about a Calculator
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       A Puzzle about a Calculator
        
       Author : surprisetalk
       Score  : 25 points
       Date   : 2024-12-30 20:50 UTC (4 days ago)
        
 (HTM) web link (aperiodical.com)
 (TXT) w3m dump (aperiodical.com)
        
       | d_tr wrote:
       | > If you allow zero width/height, you can also have 7777, 7887,
       | 7997, 7447 and 7117.
       | 
       | Why not 7227, 7337, 7557, 7667 too?
       | 
       | The theorem holds for these as well.
        
         | gamerDude wrote:
         | I assume it has to do with them being rectangular. And while
         | technically you could have a rectangle that is rotated, I think
         | it's also plausible to assume that any diagonals are considered
         | as rhombuses (rhombi?)
        
           | Someone wrote:
           | I would call 2486 and 2684 a square and, hence, a rectangle.
           | I think the theorem holds for all 8 variants of that.
        
             | feoren wrote:
             | 2486 is only a square/rectangle if the keys are exactly
             | square. They're certainly not in the example image shown.
        
         | gus_massa wrote:
         | Also 7007.
        
       | qrian wrote:
       | Any parellogram would work since given four digit number
       | n1n2n3n4, it is divisible by 11 iff n1+n3=n2+n4, and each ni is
       | linear combination of the coords of keypads xi, yi, and thus
       | (n1+n3)/2 = (n2+n4)/2
        
         | sweezyjeezy wrote:
         | Nice - the n1 + n3 = n2 + n4 equality is only necessary (mod
         | 11) e.g. 9020 works - this is because 99...99 with even # of 9s
         | is divisible by 11 and with odd # 9s is divisible by 11 if we
         | subtract 9 (or add 2) so then is = -2 mod 11. So then for
         | example with 4 digits                 1000a + 100b + 10c + d =
         | [a + b + c + d] + [999a + 99b + 9c]
         | = [a + b + c + d] - 2a - 2c (mod 11)
         | = (b + d) - (a + c) (mod 11)
        
       | russdill wrote:
       | Weird, every time I try, I just get "A suffusion of yellow"
        
         | variaga wrote:
         | That's a known bug whenever the calculated result is > 4.0.
         | Just scale down your inputs/outputs and it will work fine :)
         | 
         | (for those who don't know, the original comment is a reference
         | to the novel "The Long Dark Tea-time of the Soul" by Douglas
         | Adams)
        
       | teucris wrote:
       | At first I thought this was going to be a puzzle about getting to
       | a specific number using certain rules for navigating the pad,
       | including the operation buttons. For instance, by pressing one or
       | two buttons in each row from top to bottom, can you get the
       | calculator to display 70?
        
       | jahbrewski wrote:
       | How do you "read" an article like this? I would need to pull out
       | some paper, run calculations, etc. to understand this (but
       | perhaps I'm not the intended audience, as a non-mathematician?) -
       | Or is that how you all approach an article like this?
        
       | lilyball wrote:
       | Interestingly a 45o rotated rectangle using the keys 4 8 6 2 also
       | is divisible by 11. This isn't directly addressed in the
       | solution, although if you change "move both numbers horizontally
       | or vertically by the same distance" to say "and" instead of "or"
       | then it does.
        
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       (page generated 2025-01-03 23:01 UTC)