CPhill

Note....."2" has to be in the set.......

{2, 5, 13}  {2, 7, 11}    ...anything else???

Assuming that "0' can only be used once, let's guess that smallest 5 digit number would have to have 102 as its first three digits.

Assume that the nexrt digit might be "3"......the following digit can't be 1,2, 3.....it also can't be 4 because 10234 isn't divisible by 3 or 4....and it can't be 10235 because that isn't divisible by 2.or 3.

But, 10236  is divisible by all its non-zero digits.

Here's one possibility....the first number in the final total cost cannot be greater than 6, because that would mean that the item is more than $10

Also, the last digit  in the final toal cost must be even since 72 is an even.....and an even multiplied by an even or odd is always even.....

Then, the first digit  is either 1,2, 3, 4, 5 or 6    and the last digit is even.......a little trial and error produces

72 x $5.11   = $367.92   {the problem specifies that not all the digits are the same......but....it doesn't say that some of them couldn't be the same }

I believe this might be all the permutations of the divisors of the perfect number, "6"

Note  1 + 2 + 3  = 6  =  1* 2 *3       so...the three digit numbers are

123, 132, 213, 231 312, 321

There is an algorithm for this.....

Note that a zero is added everytime a "5" is multiplied by an even number....so....we just need to find the number of 5s that are multiplied in 75!

Divide 75 by 5 =   15

Divide 75 by 5^2   =   75  / 25   = 3

Then...there are 15 + 3  = 18  "5s" that are multiplied together in 75!......and we have more than enough even numbers to pair each 5 with....so......

Add 15 + 3     = 18 trailing zeros

lnx=1-x^3    we can write this as

e^(1 - x³)   = x

e/e^(x³)  = x

e^1  = xe^(x³)    .......notice that this is true when x = 1

1 Kilogram = 2.20462262 Pounds

So   45 x 2.20462262  = about  99.2 lbs.

5 / 53   ≈ .094 ≈  9.4%

"20% off" means "80% of"   .....and "of" means  "multiply"  ....so we have

80%  of   319   = 

.80 x 319   =  255.2

Notice the pattern......

(4-3) +( 8-6) + (12-9) + (16-12)+..........+ (96-72) + (100-75)   =

1 + 2 + 3 + 4 + ........+ 24  + 25  =     [25 * 26] / 2 =  25 * 13 =   325