JovialJman - Patterns and Logic

This genial gentleman of jovial disposition to the left is Derek Muller, as seen in this YouTube video.

Logic is defined as reasoning conducted or assessed according to strict principles of validity. While that might sound somewhat complex, people typically use this in their day to day lives in order to ascertain information that they cannot obtain by other means. However, not everyone is entirely aware of the principles behind it. Lets talk about that.

Number patterns are something that should be able to be deduced by logic, as long as you ask the right questions. In the Veritasium YouTube video Can You Solve This?, Derek Muller spoke to various people and gave them 3 numbers which follow a simple rule. He then asked these people to try and figure out what this rule is by proposing any set of 3 numbers to which Derek would confirm whether or not these additional sets followed the same rule. The numbers he started with were "2, 4, 8"; and most people thought the pattern was simply the multiplying of the previous number by 2, and so proposed 3 more numbers that followed what they believed to be the rule and then declared the rule to be such, only for Derek to tell them that it wasn't the rule. Only after he told them that they should rather try to get new information, did people start to propose sets of numbers that did not follow what they believed was the rule, thereby aiding them in finding the answer.

There was a couple that thought it was the first number to a rising power and followed their rule from there onwards which again all agreed with Derek's rule. Now his rule was any number in ascending order, which people wouldn't guess until they found 3 numbers that didn't follow that rule, ie. where one or more numbers were less than the number that came before it. The problem here is that people like to confirm what they believe rather then try and disprove it by seeking out new information. The exception to the rule being people such as Mathematicians and Scientists, who go out and try to disprove their theories and only when they cannot do so, do they think that they might be onto something.

In a separate case; if a man buys a ball and bat for R1.10 and the bat is R1 more than the ball, how much did the ball cost? This is a question that a few people get wrong. Try and guess the answer before carrying on. Now the reason people get this wrong is it isn't as straightforward as most people initially believe. The most common answer is the ball will cost 10c but this is wrong. If the ball is 10c and the bat is R1 more than the ball, then the bat will cost R1.10 and the total price will be R1.20 which is not what it actually costs. It is rather counterintuitive and thereby commonly works against common logic. (Wikipedia has good way to explain this and has other examples).

The logical way to find the problem is to go at it like this. If the total price of the 2 objects is R1.10 and one object is R1 more, then you subtract it from the total thus giving 10c, (this is where most people stop). Now since there are 2 objects, you must divide what is left by 2 giving 5c. So the ball will be 5c and the bat will be 5c plus the R1 giving R1.05. Add the 2 together and you get the original R1,10.

In yet another case while at my friend Clinton's house, he proposed a puzzle for me to solve. The pattern was as follows, "1,3,5,4,4"; "2,3,5,4,4"; "3,5,4,4"; "4,4,4"; "5,4,4,4"; "6,3,5,4,4"; "7,5,4,4" and so on. The 4 is recurring is in all cases. This was the information I started with, (well only the first one then since I didn't get anywhere he gave 4 more.). Now he did say that he would continue the pattern if I needed help but I tried to see how far I could get at first.

So I started to see what number patterns I could find. There was the 4 that came on and repeated, and 5 always lead to a 4 and 3 always leads to a 5. But that alone didn't yield a pattern the other numbers would follow. This is where Clinton said I should try think outside of the box or something to that affect. So I tried to see if I could see a pattern in the shapes of the numbers themselves, like a straighter number will lead to a curvy shape or something like that. But again I wasn't able to see anything conclusive.

Now OddballGreg tried to confuse me here and said a new pattern, A hundred, 8, 5, 4, 4, and Clinton said One hundred is actually 100,10,3,5,4,4 and this was the biggest clue so I started to think why they each said something different with the same number. Then I realized that it is spelled differently which lead to the conclusion that it is the amount of letters in the number. That is how I went about trying to deduce the answer from a rather simple pattern using logic but it is again somewhat counterintuitive.

Anyways, did you like how I solved that sequence, or did you get all of them right straight away yourself, if you did please let us know down in the comments below, or over Facebook/Twitter. If you know of someone who is a know it all and enjoys thinking, share this with them as I am sure they would like it. If you would like to see posts as they are published then please like us on the official TCSA Facebook page or follow us on Twitter with the associated buttons on the left. Thank you for reading and I hope you have/had an entertaining day. Speak again soon.

Be logical Buddies.