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Skip to 0 minutes and 0 seconds So let’s try and solve “I times KINGJO equals JOKING” We know that I is 4 so we can start by writing 4 times KINGJO and I’m going to put my dots in zeroes if you see a circle without a dot it means it’s an “O”. And this equals to JOKING, but we know that I equals 4 actually, so we can change already this into 4 and this into 4. Now, the first thing we notice is this is 6 letters or 6-digit number, and this is a 6-digit number. Multiplying a 6-digit number and getting back a 6-digit number means that this K must either be 1 or 2.

Skip to 0 minutes and 52 seconds Now, it can be both, but let’s assume that it’s 1 and see if that works out and if it doesn’t work out, then we’ll go on to 2. So, let’s assume it’s 1 and replace K with 1 throughout the problem. So we have now 4 times 14NGJO equals to JO14NG. Now, we’re going to do a bit of guessing here. We’re going to try and find some upper and lower bounds for this number over here.So, I’ll use a different colour. The lower bound for this number is 140 - now we’ve used up 1 already - so G will be 2 and J will be 3 and we’ve used up 4 so O will be 5. That’s the lower bound.

Skip to 1 minute and 42 seconds The upper bound will be 149876 so that’s the upper bound. So we know the number 14NGJO will lie anywhere between these two so consequently the answer JO14NG will be

Skip to 2 minutes and 7 seconds this times 4, so this will be between the numbers: well - 140235 times 4 is 560940 and this one is 599504. I mean we do know that this is 14, but we know that this JO14NG lies somewhere between these two numbers and we see straight away something that’s very nice - we see that the J has to be 5 and that’s the J and let’s write that. So we have now, 4 times 14NG J which is 5 O, equals, start with the J - 5O14NG Now, we know that O times 4 is going to give us] NG. And we also know that O lies between 6 and 9.

Skip to 3 minutes and 30 seconds So O lies between 6 and 9 and O times 4, well O can’t be 0 therefore it has to be either 6 or 7 or 8 or 9. O can’t be 6 because six fours are 24. That will mean that G will equal to 4, but we already got 4, so it can’t be 4! I is 4! So O perhaps is 7 - let’s try that. 4 times 14NG57 equals 5O - well we’ve just said that O is 7 so we can write here 7. 5714NG But now we have 57 times… Oh! We can do that…

Skip to 4 minutes and 23 seconds seven 4’s are 28 giving G8 which is pretty good, we have 2 that’s carried, and five 4’s are 20 so that would mean N would be 2 giving us 22 and carrying OK - and then we have 4175 - we have all the answer! and we have 75 and G times 4 plus 2 gives us 4, but wait a minute we have 2 already, so that’s 8 Yes! and we have N - that’s 2 - and indeed… 4 times 142857 is 571428 So we’ve solved the cryptarithm. So, the cryptarithm - the first part of this problem is done! 4 times 142857 equals 571428. But, what are the aliens trying to tell us?

Challenge solution

OK - so we’ve got that done. Now it’s time to wrap up the week, so go ahead, mark this step as complete and click ‘next’.

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Maths Puzzles: Cryptarithms, Symbologies and Secret Codes

Davidson Institute of Science Education at the Weizmann Institute of Science