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Divide into Primes (Posted on 2005-09-17) Difficulty: 3 of 5
The coins currently in circulation in Britain are for 1p, 2p, 5p, 10p, 20p, 50p, 100p and 200p. When I gave one of each of these coins to Tom and Harry to share between them, each took two or more coins, with each person's coins' total value equal to a prime number of pence. No coins were left over.

I asked Harry whether his share was a specific number of coins that I mentioned. He said "no".

I then asked Harry whether he had the coin of a denomination I specified. He said "yes".

His two answers allowed me to determine the total of the value that Harry had taken. What was that value?

See The Solution Submitted by Charlie    
Rating: 3.2857 (7 votes)

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My take on what Harry;s got | Comment 10 of 12 |

Remember there are only 8 coins totalling 388 ( 2 facts not specifically pointed out to us). While the total of the coins just tells us how far to search for primes and what the 2 friend's amount of money muct total...i found the number of coins available a fact which was key to my finding the solution.

1.It is necessary for the pairing of 5 & 2 to be in one of the friends hands at the end of selection...otherwise neither of them can have a prime number when all is said and done

2. Keeping in mind the value of the coins and the possible numbers that coulbe in the hundreds place tens digit and ones digit was fundamental to sifting throught a great deal of the possible primes b/t 7 and 381 (re my note about 5 &2 in on of the friend's selections being necesary and the entire total of of all the coins together as to value)  once this was done ALOT of the possibilities are automatically removed from consideration

3. 1&2 were alot easier to recognize ....remember what i said about there being _8_ coins...based on:

asked Harry whether his share was a specific number of coins that I mentioned. He said "no".

I then asked Harry whether he had the coin of a denomination I specified. He said "yes".

i concluded by elimination that he COULD and DID have the 5 and 2 pair while NOT having 5 Coins!

he mentioned the 5 to _us_  in the opening description of the problem ( i know someone hear doesnt know how the heck we can know what numbers or values he mentioned to Harry......the thing is the word mention has to do with the narrarator specifically telling us the denomination of all the coins ;-)

anyway when it all got boiled down the only answer is 107 for harry and the remainder for his friend.(381)

he coulntd have any even numbers in the 0nes'  column as there is no 2 coin total that would have given him a prime even number.

once u know he has the 5 and 2 the possible odd values in the ones place are limited to 7 (since for his friend needs a prime amount  in his toal value of couns he needs that one fols to be able to have and odd number in the ones to secure primes.

then in the tens place: ionly possibilites are 1,2 3,5,6,7,8  (as there is no carry over from the ones place and the only tens digits available are: 1,2,5 (the capacity of pr1mes is not limited

from the ones and tens;s place many of the potential answers are easily cast aside...narrow down the  primes to pairing that add to 388 and again most of the heard has been run off...

now what i said about Harry being able to have a 5 without having 5 coins .... that tells ya the rest of the story.   It was a fun puzzle, thanks for the excellent challenge Charlie.


  Posted by Rich on 2005-11-12 15:36:46
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