https://www.youtube.com/watch?v=FOOsLvSfQAY
Here ’s a fun clip from BBC Two ’s collegiate quiz showUniversity Challenge . server Jeremy Paxman postulate the objector what day of the workweek it will be 100 days after Monday . A participant identify Binnie reply quickly : “ Wednesday . ” Paxman ’s face contorts . “ How did you know that ? ” he asks , astonished .
“ Modular arithmetic , ” Binnie replies , matter - of - factly .
What ’s wonderful about this telephone exchange is that , contrary to Paxman ’s sarcastic quip , modular arithmetic – at least , to the extent that it apply to this quiz show inquiry – is middling square .
Without catch into modulo language ( for that , see see the closing of this C. W. Post ): There are seven days in a week , and seven goes into 100 days fourteen fourth dimension , with two Day leave over . Monday plus any - integer - multiple - of - seven days will bring you justly back to Monday , so this remainder of 2 days is the number Binnie “ adds ” to Monday to get his answer of Wednesday .
Written out like this , the method for solve this trouble could n’t be more obvious . So why is Paxman so astounded at Binnie ’s rapid answer ?
If I had to guess , I ’d stake that fancier forms of calendar calculation ( Kim Peek , for instance , was renown for being able to evidence you which day of the week you were born ) have conditioned us to treat dubiousness like this as heavy , and the ability to answer them quickly as indicative of initiate - levels of intelligence agency – when , in fact , if your times mesa are midway comely , the modal value of attack is actually pretty straightforward .
I ’m not saying Binnie is n’t overbold , or that his answer - clip is n’t telling ( he could be a bonafide genius for all I know , and I ’ll be the first to admit that the solution to this problem was not directly obvious to me ) . I ’m saying there ’s a deterrent example to be learn here about how we approach daunting questions , whether they ’re scientific brain-teaser , difficult tasks , or plot show queries . What I ’m saying is the difference between an insolvable problem and a tractable one can now and again be traced to our first impression of the challenge at hand . ( Preparedness , of class , never hurt . This is one of the reasonspuzzlesandbrain teaser , which condition our minds to identify familiar approaches to on the face of it unfamiliar problems , are such valuable forms of mental drill . )
https://gizmodo.com/can-you-solve-the-hardest-logic-puzzle-in-the-world-1642492269
https://gizmodo.com/youll-need-all-3-clues-to-solve-this-puzzle-1650957105
- The modular arithmetic Binnie utilize is “ arithmetical modulo 7 . ” The steps he takes can be describe by the phrase “ 100 modulo 7 , ” which can be shortened to “ 100 mod 7 , ” which basically interpret to : “ the difference you get when you divide 100 by 7 . ”
Here ’s more , from Khan Academy’s“Intro to Modular Math ” :
When we carve up two integers we will have an equation that looks like the pursual :
A / B = Q with remainder universal gas constant
A is the dividend
B vitamin is the divisor
Q is the quotient
R is the remainder
Sometimes , we are only concerned in what the end will be when we disunite A by B.
For these case there is an manipulator called the modulo operator ( abbreviated as mod ) .
Using the same A , B , Q , and R as above , we would have : A mod B = R
We would say this as “ A modulo vitamin B complex is congruous to R ” . Where B is referred to as the modulus .
For lesson we know : 13/5 = 2 residuum 3
or
13 mod 5 = 3
In the case of the video above , 100 mod 7 = 2 . Monday plus 2 days = Wednesday .
Another ready to hand elbow room to think about modular arithmetic is with with a 12 minute clock . If it ’s presently 8:00 , seven hours later it will be 3:00 ( rather than 15:00 ) , because 15 mod 12 = 3 .
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