# Fun algebra?

• MHB
Wilmer
Jack, John and CWS's
==============
Canadian Wild Strawberries (CWS) are tiny but tasty.
A and B each have a jar containing 400 CWS; they decide
to have a CWS eating race; A wins, swallowing his last
CWS when B still has 23 left. Took A 13.2 seconds; burp!
Next, B takes on C, each with a jar containing 261 CWS;
B wins, C left with 117 CWS (C has a bad toothache).
Jack: well, John, A took on C next
John: you ya I'm sure he did
Jack: each had a jar containing N CWS's
John: oh boy
Jack: want to try figure out what N is?
John: not really
Jack: here's a hint: in the 200 to 500 range, and they
both swallowed at same speed as in their 1st race
John: oh ya? (comes back with a printout)
Jack: A beat C by an integral amount
John: ya; I figured as much; need another clue
Jack: the sum of digits of the number of CWS that C had left
when A finished is equal to this number here
...and John knew.
What is the value of N?

Wilmer
Before I forget/lose my solution:

SOLUTION
Result of A:B and B:C races means A:C = 400:208.
So, for all to be integral, jars must contain a
multiple of 25, since 25:13 is lowest.
There are 13 such possibilities in the 200-500 range:
Code:
            A ate   C ate   A-C  SUMDIGITS
200     104     96     15
225     117    108      9
250     130    120      3*
275     143    132      6
300     156    144      9
325     169    156     12
350     182    168     15
375     195    180      9
400     208    192     12
425     221    204      6
450     234    216      9
475     247    228     12
500     260    240      6
Only 3 is unique as sum of digits of the differences.
So N = 250.