• Jun 10th 2010, 09:09 AM
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: 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
Mukilab
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.
• Jun 10th 2010, 02:29 PM
Wilmer
Quote:

Originally Posted by Mukilab
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.

If you're looking for such factors, then you're doing something wrong.
We're dealing with integers.
• Jun 10th 2010, 02:31 PM
Mukilab
I received a recurring decimal when finding how many strawberries A and C eat per second.
• Jun 10th 2010, 06:40 PM
Wilmer
Quote:

Originally Posted by Mukilab
I received a recurring decimal when finding how many strawberries A and C eat per second.

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
Mukilab
thanks, I didn't think of it that way :)

I'll make sure in the future to consider this
• Jun 16th 2010, 10:40 AM
Wilmer
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```
***Only 3 is unique as sum of digits of the differences.
If Jack had pointed to any of other numbers, John could not have known.
So N = 250.