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 July 26th, 2018, 05:35 PM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,632 Thanks: 954 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, 06:02 PM #2 Math Team     Joined: May 2013 From: The Astral plane Posts: 1,922 Thanks: 775 Math Focus: Wibbly wobbly timey-wimey stuff. The same as it is on MHB? When all else fails, N = 8. -Dan
July 26th, 2018, 07:45 PM   #3
Math Team

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Quote:
 Originally Posted by topsquark The same as it is on MHB?
SAME...word for word!!

 August 3rd, 2018, 10:07 AM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,632 Thanks: 954 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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