Math Is Fun Forum

Another perspective...

Cosmic Eye

Hi all;

This formula works (it's based on the one given by noelevans in post #2 of the other thread for this puzzle):

Mod(Mod(n,n-r),9)

n = a 3-digit number
r = n's row number (first row = 0)

eg,
Table 1, row 0:
Mod(Mod(856,856-0),9) = 0

Table 2, row 8:
Mod(Mod(539,539-8),9) = 8

Table 3, row 9:
Mod(Mod(273,273-9),9) = 0

My Excel table, with the 1-digit entries being results using my formula:

I had tried to solve it with base 9, but couldn't do it. However, that inspired the Mod 9 addition to noelevans' formula.

Ditto! You know how tight my BASIC programming was because of my poor little Sharp PC-1500 with its 8KB memory that I squeezed everything into but the kitchen sink!! It ran red hot!

0*1*2+3+4-5+6+7*8*9 = 512

Have to go now...catch you later.

Hi Bobby;

Correct!

I knew you'd get it. I tried to give you a bit more to do with this one, though. Did I?

0*1+2-3+4-5+6+7*8*9 = 508

Hi thickhead;

I had done something similar when I first looked at this problem and drew up two tables in Excel with 143 columns each (143 being the smallest number seemed to be as good a reason as any to stop there). There are 9 rows, as in the OP's first two tables.

My first table was for identical divisors in each column...which gave a jumbled-looking mess of results.

My second table was the one I mentioned in my previous post (incremented by 1 per row), but stretched out to 143 columns. That gave me the result I posted, which was the one that gave the most hope of containing something meaningful.

Your results appear in my second table.

That table also gave a bit of a sequence in column 6:

{343,143} mod  8 = 7;
{652,985} mod  9 = 4;
{977,327} mod 10 = 7;
{447,678} mod 11 = 7.

But I can't make anything of it, nor of anything else in my two tables.

Hi Bobby;

Correct!

Does your code solve the whole thing, including the square root and factorial components?

0*123456+7*8*9 = 504

2*9+6-7-5*1*0+483 = 500

A puzzle:

                                                       
Each letter in the sum stands for a different single-digit number from 0 to 9.
                                                                       
Find the letter values. The puzzle has a unique solution.

0-1+2-3-4*5+6+7*8*9 = 488

Hi Bobby;

There are 19 letters in the five words of my sum: ONE, TWO, FIVE, SEVEN and NINE.

Just add up all 19 values of each of the several options you haven't weeded out yet, and the total of one of them will be a factor of 486...and that one's your answer.

Have to go back outside again, into the mud. Fixing a very old retaining wall and also redirecting stormwater. May not be back till dark.

0!+ONE+TWO+3-FIVE+SEVEN-NINE+486 = 486

Substituting numbers for the corresponding words (of which there are 5) yields the post number.

A puzzle:                                                       

Each letter in the above sum stands for a different single-digit number from 0 to 9 (excluding the number 2).

The sum of the values of all 19 letters is a factor of 486.
                                                                       
Find the letter values. The puzzle has a unique solution.

Edit: My apologies to anyone who started solving the previous puzzle in this post, but this one's much better.

0*1*2-3-45+6+7*8*9 = 462
0-1+2-3+456+7-8+9 = 462
0+1-2-3+456-7+8+9 = 462
0-1+2-3+456+7-8+9 = 462
0+12-345+6+789 = 462
0+1+2+345+6*7+8*9 = 462
0-1-2-3+4+56*7+8*9 = 462
0+1-2+3-4+56*7+8*9 = 462
0*1-23+4+56*7+89 = 462
0+123*4-5-6*7+8+9 = 462
0+12-3-45-6+7*8*9 = 462

0*1+2-3+4-5+6+7*8*9 = 450