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 Post subject: Hefty hippos - a brain teaser
Unread postPosted: Tue Jan 09, 2007 6:25 am 
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A "Brain Bogglers" puzzle from the July 1990 issue of Discover magazine

Every year the members of the Loyal Order of Pygmy Hippopotami march in the Independence Day parade. When they tried on their uniforms this year, they decided that they had better lose a little weight before the Fourth. A motion was introduced, amendments were debated, and the hippos resolved to meet once a week at a gym. After the workout they'd weigh themselves and retire to their clubhouse to watch a ball game. The hippo who had lost the least number of pounds that week would have to pay for beer and pizza.
One morning they forgot to weigh themselves before leaving the gym. They found a scale in a nearby warehouse, but it started at 300 pounds, more than any of them weighed. Undaunted, they weighed all the possible pairs of hippos. At the clubhouse, they thought, it would be a simple matter to calculate the individual weights. Here are the weights of all the pairs: 361, 364, 376, 377, 380, 389, 392, 393, 396, 398, 408, 411, 414, 426, 430.

The question: How much did each hippo weigh?

You can assume that all the weights are whole numbers. If you look at them carefully, there is a relatively easy way to solve this puzzle.

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 8:49 am 
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First step: Number of Hippos

There are 15 numbers, if the hippos were weighed in pairs, there were 30 occasions on the scale and 6 hippos, each weighed 5 times.

Second step: How on earth to separate the numbers:

Because this is a maths quizz, carefull scrutiny of the numbers themselves is required, and there is an anominally, there are 5 odd numbers and 10 even numbers. Remembering that each hippo was weighed 5 times, we can summize that one hippo's wieght is different to the others in terms of odds and evens.

Third step: Seperating the numbers:


The 5 odd numbers added together should therefore equal:
5a + b + c + d + e + f = 1931

The remaining numbers should then equal:
4b + 4c + 4d + 4e + 4f = 3984

Therefore:

5a + b + c + d + e + f = 1931
4b + 4c + 4d + 4e + 4f = 3984
b + c + d +e + f = 3984/4 = 996

5a + 996 = 1931
5a = 935
a = 187

The remaining hippos weights can then be found by subtracting the one hippos weight from the 5 odd numbers.

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Unread postPosted: Tue Jan 09, 2007 8:59 am 
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First, since there were 15 possible pairs that means there were six hippos. Each hippo got on the scale exactly five times.
Among the weight pairs are five odd numbers. This means either that one hippo's weight was odd and all the rest were even, or that one was even and the rest odd. It doesn't matter which; it still singles out one hippo from the rest. The five odd numbers represent one hippo's weight added to each of the other five's. Therefore, the sum of the odd numbers--1,931--equals five times the singled-out hippo's weight plus the sum of the other five hippos' weights. The ten even numbers represent the weights of the five remaining, each added to each of the other four. Since each of these five was added to four others, the sum of the even numbers--3,984--equals four times the sum of the five hippos' weights.

That sum comes to 996. Now subtract that from the sum of the odd numbers: the difference is 935. Divide that by five and you will have the weight of the singled-out hippo, 187 pounds. From that it is an easy matter to derive the weights of the other five hippos. Simply subtract 187 from each of the five odd numbers.

The six hippos turn out to weigh 174, 187, 190, 202, 206, and 224 pounds
Source Hippo World

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 9:52 am 
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There ARE two ways of solving the puzzle, surfing the web or doing it with Algebra - both ways are fun... though not equally so... for some :twisted: :lol:

Loved your efforts!

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 10:15 am 
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More important questions remain other than the weight of the Hippos

1. Who in their right minds would want to weigh Hippo's????
2. Will they get offended if they get told they are fat???
3. Would I want to be the one to tell them??
4. Once the fattest one figures out that he is in fact the fattest... Would I want to be in the same room??

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 10:55 am 
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Why did the hippo cross the road?


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Unread postPosted: Tue Jan 09, 2007 11:05 am 
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1. To get to the other side?
2. To show that it can be done?
3. To proove that he is chicken?

Pray tell... :lol:

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 11:10 am 
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I would I know?


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 Post subject:
Unread postPosted: Tue Jan 09, 2007 11:25 am 
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To find a scale that's easier to use...

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 11:33 am 
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gwendolen wrote:
would I know?


I'm not going THERE... :twisted:

...although I think you can be the butt of a joke without feeling agrieved... :lol:

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 12:27 pm 
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:hmz:


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 Post subject:
Unread postPosted: Tue Jan 09, 2007 1:09 pm 
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gwendolen shows indecision, wrote:
:hmz:


:lol: Reaction not TOO severe, gwendolen. Thanks for letting me get off that lightly :lol:

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 Post subject:
Unread postPosted: Tue Jan 09, 2007 1:14 pm 
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Johan looking for trouble wrote:
Thanks for letting me get off that lightly :lol:


You just used up your quota for this year. :twisted:


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Unread postPosted: Tue Jan 09, 2007 2:20 pm 
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Here's another teaser - easier than the first - let's see if you can surf to an answer...

A young hippo is being weaned. He starts to eat one leaf on the first day of his weaning, which is also the first day of that month; two on the second day, three on the 3rd day, increasing the number of leaves by one every day. After having eaten his quota on the last day of the month, the hippo had consumed a total of 406 leaves. During which month was he weaned?

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Unread postPosted: Tue Jan 09, 2007 3:41 pm 
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