I got as far as working out how many A and C ate per second but now I'm at a semi-standstill as I attempt to figure out how to find factors of fractions/recurring decimals.

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- Jun 10th 2010, 09:09 AM #1

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## Canadian wild strawberries

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 integer 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?

- Jun 10th 2010, 12:38 PM #2

- Jun 10th 2010, 02:29 PM #3

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- Jun 10th 2010, 02:31 PM #4

- Jun 10th 2010, 06:40 PM #5

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So?

The "number per second" does not matter.

What is needed is the A:C ratio; calculated from the given A:B and B:C ratios:

A / B = 400 / 377 ; B / C = 261 / 144 .... so A / C = 25 / 13 :

in other words, when A eats 25, C eats 13.

You're told range is 200 to 500; so you need to find the integer cases; there are 13:

1) 200 : 104 ; diff = 96 ; sumdigits = 15

2) 225 : 117 ; diff = 108; sumdigits = 9

....

13) 500 : 260 ; diff = 240; sumdigits = 6

- Jun 11th 2010, 04:06 AM #6

- Jun 16th 2010, 10:40 AM #7

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SOLUTION:

Result of A:B and B:C races means A:C = 400:208.

So, as we're dealing with integers, 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

If Jack had pointed to any of other numbers, John could not have known.

So N = 250.