Est. 1998 — 27 years of woodworking knowledge
Friday puzzle -- a little early again this week
Alex Y
LUMBER is a six-digit number, with six distinct non-zero digits.
When divided by 19, the remainder is 17
When divided by 17, the remainder is 13
When divided by 13, the remainder is 11
When divided by 11, the remainder is 7, and
When divided by B, the reminder is M.
What is ELM?
Re: Friday puzzle -- a little early again this wee
David Weaver
I missed this yesterday...so i'll admit I got lazy and set up the equations in solver (excel) and tried to find a unique solution.
However, solver is a first moment approximation, so it doesn't come up with anything.
Stab #2 is going to be setting up a system of equations where the number is equal to:
L*100000 + u*10000 + m*1000 + b*100 + e*10 + r
Then we can start setting up
Lumber mod 19 = 17
...
looks like work so far!
Re: Friday puzzle -- a little early again this wee
David Weaver
hmmm...all of the remainders are primes and all of the divisors are primes....
Re: Friday puzzle -- a little early again this wee
Alex Y
Probably more significant that the divisors are all prime than that the remainders are. Actually, relatively prime would be sufficient.
Solution
Alex Y
The first four conditions give you the fact that "LUMBER" is equal to
20,005 Mod 46,189.
(I found this out via spreadsheet, but those in the know tell me it is the result of the Chinese Remainder Theorem)
There are only 20 such six-digit numbers, and only two of those, 389,517 and 943,785, have six distinct non-zero digits.
You can't divide a number by 5 and have a remainder of 9, so that rules out
389,517. But just to check, 943,785/7=123,826, remainder 3.
So ELM = 893