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July 26th, 2018, 05:35 PM   #1
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Fun algebra?

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: ya ya I'm sure he did
Jack: each had a jar containing N CWS's
John: oh boy
Jack: wanna 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?
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July 26th, 2018, 06:02 PM   #2
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Math Focus: Wibbly wobbly timey-wimey stuff.
The same as it is on MHB?

When all else fails, N = 8.

-Dan
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July 26th, 2018, 07:45 PM   #3
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Quote:
Originally Posted by topsquark View Post
The same as it is on MHB?
SAME...word for word!!
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August 3rd, 2018, 10:07 AM   #4
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Before I forget or 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.
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