WEBVTT
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So let's try and solve "I times KINGJO equals JOKING"
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We know that I is 4 so we can start by writing
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4 times KINGJO
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and I'm going to put my dots in zeroes
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if you see a circle without a dot it means it's an "O".
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And this equals to JOKING, but we know
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that I equals 4 actually, so we can change already this into 4
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and this into 4.
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Now, the first thing we notice is this is 6 letters or 6-digit number, and this is a 6-digit number.
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Multiplying a 6-digit number and getting back a 6-digit number means
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that this K must either be 1 or 2.
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Now, it can be both, but let's assume that it's 1 and see if that works out
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and if it doesn't work out, then we'll go on to 2.
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So, let's assume it's 1 and replace K with 1 throughout the problem.
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So we have now 4 times 14NGJO
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equals to JO14NG.
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Now, we're going to do a bit of guessing here.
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We're going to try and find some upper and lower bounds
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for this number over here.So, I'll use a different colour.
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The lower bound for this number is 140 - now we've used up 1 already -
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so G will be 2 and J will be 3 and we've used up 4 so O will be 5.
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That's the lower bound. The upper bound will be
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149876
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so that's the upper bound. So we know the number 14NGJO will lie anywhere between these two
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so consequently the answer JO14NG will be
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this times 4, so this will be between the numbers:
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well - 140235 times 4 is
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560940
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and this one is 599504.
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I mean we do know that this is 14, but we know that
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this JO14NG lies somewhere between these two numbers
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and we see straight away something that's very nice -
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we see that the J has to be 5
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and that's the J
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and let's write that.
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So we have now, 4 times 14NG J which is 5 O,
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equals, start with the J - 5O14NG
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Now, we know that O times 4 is going to give us]
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NG. And we also know that
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O lies between 6 and 9.
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So O lies between 6 and 9 and
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O times 4, well O can't be 0 therefore it has to be either 6 or 7 or 8 or 9.
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O can't be 6 because six fours are 24.
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That will mean that G will equal to 4, but we already got 4,
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so it can't be 4! I is 4!
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So O perhaps is 7 - let's try that.
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4 times 14NG57
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equals 5O - well we've just said that O is 7 so we can write here 7.
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5714NG
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But now we have 57 times... Oh! We can do that...
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seven 4's are 28 giving G8 which is pretty good,
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we have 2 that's carried, and five 4's are 20
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so that would mean N would be 2 giving us 22 and carrying
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OK - and then we have
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4175 - we have all the answer!
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and we have 75 and G times 4
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plus 2 gives us 4, but wait a minute we have 2 already, so that's 8
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Yes! and we have N - that's 2 - and indeed...
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4 times 142857 is 571428
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So we've solved the cryptarithm.
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So, the cryptarithm - the first part of this problem is done!
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4 times 142857 equals 571428.
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But, what are the aliens trying to tell us?