Math Is Fun Forum

damzel

Member

Registered: 2007-01-04

Posts: 2

logic puzzles~help

logic puzzles are so difficult i was wondering if someone could help me solve these two problems.

the first one is:

1) Ms. Nelson’s first-grade is learning how to count money. Today, Ms. Nelson filled each of 20 envelopes with a different combination of pennies, nickels, dimes, and quarters. She then handed four of the envelopes to each of five children (one is Beau). Each child’s envelopes are four different colors (blue, green, red, and yellow). Each envelope contained three coins and after the five children counted the money, they found that each had been given the same total amount of money. Can you determine the full name of each child and the amount of money in each of his or her envelopes?
    1) One child has an envelope containing three times as much money as one of his or her other envelopes, which contains more than twice as much money as each of his or her two other envelopes.
    2)One child has an envelope containing coins worth three times as much as those in one of his or her other envelopes, which are worth half as much as the coins in one of his or her other envelopes.
    3) The yellow envelope of the one surnamed Meyer is worth twice as much as Candy’s red envelope, which is worth twice as much as the Lord child’s green envelope
    4) One green envelope contains twice as much money as a blue envelope.
    5) The Smith child’s yellow envelope contains $0.10 more than Emily’s red envelope, which contains $0.10 more than Derek’s green envelope, which contains $0.10 more than Jones child’s blue envelope.
    6) Alex’s green envelope contains $0.10 less than the white child’s red envelope, which contains $0.10 less than the Smith child’s blue envelope.
    7) Each child has more money in his or her yellow envelope than in his or her blue envelope.

the second one is:

2) When Joe hit a bit of writer’s block and decided to break for lunch, he left the main character of his newest murder mystery, Clueless, in quite a quandary. Professor Danvers had hosted what he though would be a festive house party for six of his dearest friends, but the disappearance of one of the guests, Mr. Boddy, put a damper on the whole affair! After a weekend of puzzling over the bizarre circumstances, the five remaining guest departed on Sunday evening, only to contact Professor Danvers through an urgent e-mail first thing in the morning of a different day of the following week (from Monday through Friday). It seems that each guest had left behind a different, rather curious item (including a wrench) and was seeking its immediate return. Danvers conducted a search of his mansion on each of the five afternoons of that week, and although not every day’s search yielded an item, and although some items may have been found before they were reported missing, all of them were eventually found. Each item was discovered in a different location (including behind the draperies) in a different room (one is the billiards room) of the mansion. Can you determine the day on which Professor Danvers received an e-mail from each guest, as well as match each guest with his or her item, the day on which his or her item was found, and the location and room in which the item was discovered.
   
    1) Three items found on consecutive days, in order from first to last, are Mrs. Hepplewhite’s item, the item that was uncovered behind the potted palm, and the jump rope.
    2) On three consecutive days, in order from first to last, Professor Danvers received an e-mail from Madame Primrose, located an item in the dining room, and received an e-mail regarding the item that was located under the cushions of a chaise lounge.
    3) One morning, Professor Danvers received a message requesting the return of a lead pipe (“It’s my favorite walking stick, but admittedly a bit heavy”), and that afternoon, his butler moved the armoire in the ballroom and found an item that had been reported missing the day before.
    4) Captain Longhorn’s email arrived the day after the one that concerned the item that turned up in the conservatory and the day before the message about the missing knife (It’s perfect for buttering my croissants”)
    5) One afternoon, Professor Danvers was surprised to stumble across an item under one of his prized Oriental rugs, as he had not yet learned of its loss.
    6) Both Lady Marshfield’s item and the jump rope were found on the same afternoon, but, to Professor Danver’s dismay, the next day’s search yielded none of the missing items.
    7) The item found in the library on Friday afternoon was reported missing at least twenty-four hours before its retrieval.
    8) The missing candlestick (“ One never knows when there will be a power failure”) showed up at least one day before Dr. Greyson’s item was found; Dr. Greyson’s item was found the day before his e-mail laws received.

hope someone can help, im kinda desperate...

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: logic puzzles~help

I've made a start on the first one.

I made a list of all the possible combinations of 3 coins that could be in the envelopes, and it turned out that there were exactly 20. This is very useful because it means that each of those combinations is used exactly once.

Here they all are, in order of price:

All of these add up to give a total of 615, and as each child gets the same amount of money in total, we can deduce that they get given envelopes totalling 123 each.

The first clue says that one child gets an envelope worth 3 times as much as one of their others, and that that one is worth more than twice as much as the other two. The only set that fits that condition and can also get as high as 123 is {11, 12, 25, 75}.

The second clue says that one child has an envelope worth 3 times as much as one of their others, and that that one is worth half as much as another of their others. This means that three of their 4 envelopes are of the form n, 2n, 3n.
The only two sets of envelopes like this are {15, 30, 45} and {20, 30, 60}. However, the first of these would require an envelope worth 33 to make the total equal 123, and there is no envelope like this. Therefore, their set of envelopes is {3, 20, 40, 60}.

And that's as far as I've got. Hopefully that helps a bit.

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Why did the vector cross the road?
It wanted to be normal.

damzel

Member

Registered: 2007-01-04

Posts: 2

Re: logic puzzles~help

^^ thank for the help, at least it will get me started