Friday Puzzler -- ABCDEF

Re: Friday Puzzler -- ABCDEF

Larry Barrett

I think A must be 1. If 2 or greater, then 5A and 6A would be 2 digit numbers.

So far I can't think of a way other than trial and error to find the right combination of digits for BCDEF.

Re: Friday Puzzler -- ABCDEF

Sam Force

142... Google is my friend could not get it myself

Re: Friday Puzzler -- ABCDEF

Alex Y

Correct on A

The next one you can deduce is F.

I'll leave the hints at that for now, but there is a systematic solution process, with very little trial and error.

Re: Friday Puzzler -- ABCDEF

Alex Y

Probably right, but I won't check it against the answer I have (which is unique, so I'm sure they are the same).

Thanks for not posting the full answer -- letting others continue to try without google.

Hint

Alex Y

Before finding A, you could narrow the possibilities for F to three digits. After finding A, only one of those will work.

Hint 2 Solution order

Alex Y

Solve in this order:

A (Larry correctly deduced this to be 1)

F

The rest of column F

The rest of column A

At this point, you will know what digits are represented by B,C,D, and E, and you just have to figure out which is which. Going either left to right or right to left, you can figure out which digit will work in each place, with just a little trial and error.

Re: Hint 2 Solution order

Larry Barrett

F could be any of the digits 0, 1. 2. ... 9.

To find out which are possible, multiply each by the numbers 1, 2, ... 6. Examine the 'ones' place in the answers. There can not be any repeats in the 'ones' place because of the way the problem is stated. So, for instance, F can not be 5 because 5 multiplied by 1, 2, .. 6 is 5, 10, 15, 20, 25, 30 and we see that the digit 5 is repeated several times in the 'ones' column. Similarly, 0, 2, 4, 5, 6, 8 can all be eliminated for F. But F could be 1, 3, 7, or 9. We already know that A is 1, so F could still be 3, 7, 9.

We do know that the digit 1 must appear in the 'ones' place in the F column because it also appears in the A column (1x1=1 and there would be no carry from column B). By examining 3 and 9 each multiplied by 1, 2, ...6 we can see that 1 does not appear in the 'ones' column. F must therefore be 7. And when examining the 'ones' column for F, we can see that the remaining numbers for B, C, D, and E must be 4, 8, 5, 2, in some order.

Now, cheating a bit and making use of Sam's hint, we can guess that B=4 and C=2. It remains to try 8 and 5 for D and E.

First guess is D=8 and E=5.

With my handy Sharp calculator, entering 142857 and saving it in memory, then multiplying that by 1, 2, ... 6 I see those same digits repeated in the answer, in different order.

So ABCDEF is 142857.

Correct!

Alex Y

And these numbers are the repeating digits in 1/7. The other rows are 2/7, 3/7, 4/7, 5/7, and 6/7, which have the same repeating digits, just starting with a different one.