Ooh, this is a good one. Couple early thoughts: 1. By the time the puzzle said "divisible by 9," the reader could already have deduced that fact. 2. The middle digit is 5.
Got it, with quite a bit of trial and error. There may be a better way of going about it, and a real mathematician might be able to prove or disprove that there is more than one solution, but I got there even through Long Covid brain fog while halfway watching Christmas football.
In addition to the hints above, you can deduce that it has to alternate odd and even digits since an odd number is not evenly divisible by an even number, so it has to fit this template: oeoe5eoeo
Notes on my method (probably sloppy but I got there): There are many (but still limited) combinations for the first 3, (any odd except 5, any even, any odd other than 5 and the odd in position 1, to make the sum of the 3 digits a multiple of 3.) After that, take your working number and -multiply it by 10, -divide by the next divisor, -subtract the whole number, -multiply the leftover fraction by the divisor, -figure out how much you need to add to get the result to = the divisor. -If that number is still available (and fits the even/odd progression) use it and keep going -if you hit a wall, back up and try again.
Frustratingly I had one that ALMOST worked up through the 8th digit but failed: 1472583*6*9
Rob Brown (Sorry to keep posting as anonymous several times over the last couple weeks. I keep getting an error that insists that I need to change my browser settings to use my Google account and I am not willing to do that.)
9 equations with 9 unknowns with 9 conditions. let X = A+B+C+D+E+F+G+H+I and X is divisible by 9, etc. Then Y = A+B+C+D+E+F+G+H and Y is divisible by 8, etc
Set it up as a matrix and matrix math will find the solution in like 3 steps (but it helps to use a computer to do so)
Ooh, this is a good one. Couple early thoughts:
ReplyDelete1. By the time the puzzle said "divisible by 9," the reader could already have deduced that fact.
2. The middle digit is 5.
Got it, with quite a bit of trial and error. There may be a better way of going about it, and a real mathematician might be able to prove or disprove that there is more than one solution, but I got there even through Long Covid brain fog while halfway watching Christmas football.
ReplyDeleteIn addition to the hints above, you can deduce that it has to alternate odd and even digits since an odd number is not evenly divisible by an even number, so it has to fit this template:
oeoe5eoeo
Notes on my method (probably sloppy but I got there):
There are many (but still limited) combinations for the first 3, (any odd except 5, any even, any odd other than 5 and the odd in position 1, to make the sum of the 3 digits a multiple of 3.)
After that, take your working number and
-multiply it by 10,
-divide by the next divisor,
-subtract the whole number,
-multiply the leftover fraction by the divisor,
-figure out how much you need to add to get the result to = the divisor.
-If that number is still available (and fits the even/odd progression) use it and keep going
-if you hit a wall, back up and try again.
Frustratingly I had one that ALMOST worked up through the 8th digit but failed:
1472583*6*9
Rob Brown
(Sorry to keep posting as anonymous several times over the last couple weeks. I keep getting an error that insists that I need to change my browser settings to use my Google account and I am not willing to do that.)
9 equations with 9 unknowns with 9 conditions. let X = A+B+C+D+E+F+G+H+I and X is divisible by 9, etc. Then Y = A+B+C+D+E+F+G+H and Y is divisible by 8, etc
ReplyDeleteSet it up as a matrix and matrix math will find the solution in like 3 steps (but it helps to use a computer to do so)