July 26th, 2018, 04:35 PM  #1 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934  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? 
July 26th, 2018, 05:02 PM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 1,889 Thanks: 768 Math Focus: Wibbly wobbly timeywimey stuff. 
The same as it is on MHB? When all else fails, N = 8. Dan 
July 26th, 2018, 06:45 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934  
August 3rd, 2018, 09:07 AM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,296 Thanks: 934 
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 200500 range: Code: A ate C ate AC 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 So N = 250. 

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