Grades 7-8 Video Solutions 2024-2024_7-8

Video Transcription

Problem number one, which of the following strings cannot be transformed into the string on the right without cutting?  So the first thing that we can do is notice that the string on the right is not actually a knot It's just a loop that has been twisted and below I've enlarged all the pictures  so we can first see that in option a we can undo both of these loops by sort of twisting these loops and  Pulling one end to the left and the other end to the right and if we do that for both of the loops  Then we will be able to undo this loop completely and it'll just be a single loop of string. That's not a knot  Similarly for option C We can pull this left loop out of the other loops and as a result We will have a single loop of string that is not a knot by the same logic in D  we can pull out this loop of string and that will also make a single loop that it's not a knot and  Finally in E we can also twist the ends of the loop so that they will not be a knot  So the only one that's left is option B and in fact, this is what's known as a trefoil knot or a trefoil knot  This is a knot that we cannot undo it just by pulling on the string the only way that we can make into a loop is by cutting the string and  Reattaching it together. So that means that the answer is B

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