## Enigma 1412 - Any Amount

NewScientist Enigma 1412 - Oct 7 2006 by Albert Haddad

I have a five-digit TOTAL, stuff a six-digit AMOUNT and several other whole numbers, all expressed in words written in capital bold letters, where dfif letters stand for diff digits and the same letters stands for the same digit.

A few curious properties are noticeable. For instance, if you add ANY amount to my TOTAL, and then divide by say, A value, the result is a whole number.

And if you subtract AN amount from my AMOUNT, and then divide by say ANY value the result of course is ANY amount.

How much is my five-digit VALUE?

I solved it quickly but I realized that I had received the issue almost after a month it was actually sent so I couldn’t take part in their competition draw!

My answer was : **VALUE = 89140**

After I confirm this answer in the next issue of the magazine I’ll post how I deduced this.

**CONFIRMED on Nov 20**!

1. First I deduced from second condition that AMOUNT = ANY*ANY + AN

2. Now I wrote this simple perl program to iterate three digit unique values which produce unique six digit sum:

for my $i ( 317 .. 999 )

{

next if &repeat ($i);

my $s = $i * $i + substr ($i,0,2);

next if &repeat ($s);

next if substr ($s,0,1 ) ne substr ($i,0,1);

next if substr ($s,4,1) ne substr ($i,1,1);

print "ANY=$i : AMOUNT=$s

";

}

*repeat* just checks to make sure there was no duplicate in the number itself.

3. I got two results:

ANY=963 : AMOUNT=927465

ANY=976 : AMOUNT=952673

4. Discarding second one because we have same codes for ‘Y’ and ‘U’.

5. Leaving only only one result! Common sense suggested that V cannot be 0 thus: L=1 M=2 Y=3 U=4 T=5 N=6 O=7 A=9 V=8 E=0

6. Net result was confirmed to be 89140