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## #2 Re: Ganesh's Puzzles » Oral puzzles » 2016-06-01 19:15:46

Hi (:

Agreed with bobbym, unless a and b are both zero. That just leaves y = (4-3x)/5

## #3 Re: Exercises » True or False easies » 2016-06-01 18:58:15

I am getting the same answer (:

## #4 Re: Exercises » Quickies #1 Math » 2016-06-01 18:45:58

Hey;

1. I agree with bobbym

## #5 Re: Help Me ! » Geometry » 2016-05-22 20:48:58

Quite a distance (:

## #6 Re: Help Me ! » Two-blocks number » 2016-05-14 22:11:02

I verified the answer as well and like chen.aavaz only missed it because of the size of a. n = 36. Well done (:

## #7 Re: Help Me ! » Two-blocks number » 2016-05-13 08:28:04

Having trouble finding any more integer results. It seems likely that a is bigger than 10^12....

## #8 Re: Help Me ! » Two-blocks number » 2016-05-13 07:59:54

Oh, I see. I will keep looking

## #9 Re: Help Me ! » Two-blocks number » 2016-05-13 07:46:39

Hi, I don't understand... is the problem not just to choose three positive integers such that a=(k+10^n)/(k+1)^2 ?

## #10 Re: Help Me ! » Two-blocks number » 2016-05-13 07:32:14

Hi! I found three answers so far:

1. Set k=8, n=8, a=1234568, b=9876544,
c=123456809876544

2. Set k=10, n=12, a=8264462810, b=82644628100,
c=8264462810082644628100

3. Set k=40, n=10, a=5948840, b=237953600,
c=59488400237953600

Further answer:

4. Set k=188, n=6, a=28, b=5264,
c=28005264

## #11 Re: Help Me ! » Two-blocks number » 2016-05-13 01:29:29

Hi, I don't know if this was apparent already, and it's not a big clue, but I confirmed experimentally that at least one of a, k or n is greater than 100.

## #12 Re: Dark Discussions at Cafe Infinity » Significant Individuals (crème de la crème #2) » 2016-05-07 05:37:45

#39. Michelangelo

Michelangelo di Lodovico Buonarroti Simoni (March 1475 – 18 February 1564), was an Italian sculptor, painter, architect, poet, and engineer of the High Renaissance who exerted an unparalleled influence on the development of Western art. Considered to be the greatest living artist during his lifetime, he has since also been described as one of the greatest artists of all time. Despite making few forays beyond the arts, his versatility in the disciplines he took up was of such a high order that he is often considered a contender for the title of the archetypal Renaissance man, along with contemporary rival and fellow Florentine Medici client, Leonardo da Vinci.

A number of Michelangelo's works in painting, sculpture, and architecture rank among the most famous in existence. His output in every field of interest was prodigious; given the sheer volume of surviving correspondence, sketches, and reminiscences taken into account, he is the best-documented artist of the 16th century.

Two of his best-known works, the Pietà and David, were sculpted before the age of thirty. Despite his low opinion of painting, Michelangelo also created two of the most influential frescoes in the history of Western art: the scenes from Genesis on the ceiling of the Sistine Chapel in Rome, and The Last Judgment on its altar wall. As an architect, Michelangelo pioneered the Mannerist style at the Laurentian Library. At the age of 74, he succeeded Antonio da Sangallo the Younger as the architect of St. Peter's Basilica. Michelangelo transformed the plan,with the western end being finished to his design, and the dome being completed after his death, with some modification.

In a demonstration of Michelangelo's unique standing, he was the first Western artist whose biography was published while he was alive. Two biographies were published of him during his lifetime; one of them, by Giorgio Vasari, proposed that he was the pinnacle of all artistic achievement since the beginning of the Renaissance, a viewpoint that continued to have currency in art history for centuries.

In his lifetime he was also often called Il Divino ("the divine one"). One of the qualities most admired by his contemporaries was his terribilità, a sense of awe-inspiring grandeur, and it was the attempts of subsequent artists to imitate Michelangelo's impassioned and highly personal style that resulted in Mannerism, the next major movement in Western art after the High Renaissance.

Michelangelo, with Leonardo da Vinci and Raphael, is one of the three giants of the Florentine High Renaissance. Although their names are often cited together, Michelangelo was younger than Leonardo by 23 years, and older than Raphael by eight. Because of his reclusive nature, he had little to do with either artist and outlived both of them by more than forty years. Michelangelo took few sculpture students. He employed Francesco Granacci, who was his fellow pupil at the Medici Academy, and became one of several assistants on the Sistine Chapel ceiling. Michelangelo appears to have used assistants mainly for the more manual tasks of preparing surfaces and grinding colours. Despite this, his works were to have a great influence on painters, sculptors and architects for many generations to come.

While Michelangelo's David is the most famous male nude of all time and destined to be reproduced in order to grace cities around the world, some of his other works have had perhaps even greater impact on the course of art. The twisting forms and tensions of the Victory, the Bruges Madonna and the Medici Madonna make them the heralds of the Mannerist art. The unfinished giants for the tomb of Pope Julius II had profound effect on late-19th- and 20th-century sculptors such as Rodin and Henry Moore.

Michelangelo's foyer of the Laurentian Library was one of the earliest buildings to utilise Classical forms in a plastic and expressive manner. This dynamic quality was later to find its major expression in Michelangelo's centrally planned St Peter's, with its giant order, its rippling cornice and its upward-launching pointed dome. The dome of St Peter's was to influence the building of churches for many centuries, including Sant'Andrea della Valle in Rome and St Paul's Cathedral, London, as well as the civic domes of many public buildings and the state capitals across America.

Artists who were directly influenced by Michelangelo include Raphael, who imitated Michelangelo's prophets in two of his works, including his depiction of the great master in the School of Athens. Other artists, such as Pontormo, drew on the writhing forms of the Last Judgement and the frescoes of the Capella Paolina.

The Sistine Chapel ceiling was a work of unprecedented grandeur, both for its architectonic forms, to be imitated by many Baroque ceiling painters, and also for the wealth of its inventiveness in the study of figures. Vasari wrote: "The work has proved a veritable beacon to our art, of inestimable benefit to all painters, restoring light to a world that for centuries had been plunged into darkness. Indeed, painters no longer need to seek for new inventions, novel attitudes, clothed figures, fresh ways of expression, different arrangements, or sublime subjects, for this work contains every perfection possible under those headings."

## #13 Re: Dark Discussions at Cafe Infinity » Significant Individuals (crème de la crème #2) » 2016-05-07 05:31:54

#38. Henry Adams

Henry Brooks Adams (February 16, 1838 – March 27, 1918) was an American historian and member of the Adams political family, being descended from two U.S. Presidents.

As a young Harvard graduate, he was secretary to his father, Charles Francis Adams, Abraham Lincoln’s ambassador in London, a posting that had much influence on the younger man, both through experience of wartime diplomacy and absorption in English culture, especially the works of John Stuart Mill. After the American Civil War, he became a noted political journalist who entertained America’s foremost intellectuals at his homes in Washington and Boston.

In his lifetime, he was best known for his History of the United States During the Administrations of Thomas Jefferson and James Madison, a 9-volume work, praised for its literary style.

His posthumously published memoirs, The Education of Henry Adams, won the Pulitzer Prize and went on to be named by The Modern Library as the top English-language nonfiction book of the twentieth century.

In 1868, Henry Adams returned to the United States and settled in Washington, D.C., where he began working as a journalist. Adams saw himself as a traditionalist longing for the democratic ideal of the 17th and 18th centuries. Accordingly, he was keen on exposing political corruption in his journalism.

Adams said, "I think that Lee should have been hanged. It was all the worse that he was a good man and a fine character and acted conscientiously. It's always the good men who do the most harm in the world."

In 1870, Adams was appointed Professor of Medieval History at Harvard, a position he held until his early retirement in 1877 at 39. As an academic historian, Adams is considered to have been the first (in 1874–1876) to conduct historical seminar work in the United States. Among his students was Henry Cabot Lodge, who worked closely with Adams as a graduate student.

On June 27, 1872, he and Clover Hooper were married in Beverly, Massachusetts, and spent their honeymoon in Europe, much of it with Charles Milnes Gaskell at Wenlock Abbey in Shropshire, England. Upon their return, he went back to his position at Harvard, and their home at 91 Marlborough Street, Boston, became a gathering place for a lively circle of intellectuals. Adams was elected a Fellow of the American Academy of Arts and Sciences in 1875. In 1877, he and his wife moved to Washington, D.C., where their home on Lafayette Square, across from the White House, again became a dazzling and witty center of social life. He worked as a journalist and continued working as a historian.

Adams's The History of the United States of America (1801 to 1817) (9 vols., 1889-1891) has been called "a neglected masterpiece" by Garry Wills, and "A history yet to be replaced" by C. Vann Woodward. It is a highly detailed history of the Jefferson and Madison administrations, with a focus on diplomacy. There is wide praise for its literary merit, especially the opening five chapters of volume 1, describing the nation in 1800. These chapters have also been criticized; Noble Cunningham states flatly, "Adams misjudged the state of the nation in 1800." In striving for literary effect, Cunningham argues, Adams ignored the dynamism and sophistication of the new nation.

In the 1880s Adams wrote two novels, starting with Democracy, which was published anonymously in 1880 and immediately became popular. (Only after Adams's death did his publisher reveal his authorship.) His other novel, published under the nom de plume of Frances Snow Compton, was Esther, whose heroine was believed to be modeled after his wife.

Adams was a member of an exclusive circle, a group of friends called the "Five of Hearts" that consisted of Henry, his wife Clover, geologist and mountaineer Clarence King, John Hay (assistant to Lincoln and later Secretary of State), and Hay's wife Clara. One of Adams's frequent travel companions was the artist John La Farge, with whom he journeyed to Japan and the South Seas. A long-time, intimate correspondent of Adams's was Elizabeth Cameron, wife of Senator J. Donald Cameron.

In 1894, Adams was elected president of the American Historical Association. His address, entitled "The Tendency of History", was delivered in absentia. The essay predicted the development of a scientific approach to history, but was somewhat ambiguous as to what this achievement might mean.

In 1904, Adams privately published a copy of his "Mont Saint-Michel and Chartres", a pastiche of history, travel, and poetry that celebrated the unity of medieval society, especially as represented in the great cathedrals of France. Originally meant as a diversion for his nieces and "nieces-in-wish", it was publicly released in 1913 at the request of Ralph Adams Cram, an important American architect, and published with support of the American Institute of Architects.

He published The Education of Henry Adams in 1907, in a small private edition for selected friends. For Adams, the Virgin Mary was a symbol of the best of the old world, as the dynamo was a representative of modernity. It was only following Adams's death that The Education was made available to the general public, in an edition issued by the Massachusetts Historical Society. It ranked first on the Modern Library's 1998 list of 100 Best Nonfiction Books and was named the best book of the twentieth century by the Intercollegiate Studies Institute, a conservative organization that promotes classical education. It was awarded the Pulitzer Prize in 1919.

In 1912, Adams suffered a stroke, perhaps brought on by news of the sinking of the Titanic, for which he had return tickets to Europe. After the stroke, his scholarly output diminished, but he continued to travel, write letters, and host dignitaries and friends at his Washington, D.C., home. Henry Adams died at age 80 in Washington, D.C. He is interred beside his wife in Rock Creek Cemetery, Washington.

## #14 Re: Dark Discussions at Cafe Infinity » Significant Individuals (crème de la crème #2) » 2016-05-07 05:24:13

#37. Napoleon

Napoléon Bonaparte (born Napoleone di Buonaparte; 15 August 1769 – 5 May 1821) was a French military and political leader who rose to prominence during the French Revolution and led several successful campaigns during the Revolutionary Wars. As Napoleon I, he was Emperor of the French from 1804 until 1814, and again in 1815. Napoleon dominated European and global affairs for more than a decade while leading France against a series of coalitions in the Napoleonic Wars. He won most of these wars and the vast majority of his battles, building a large empire that ruled over continental Europe before its final collapse in 1815. Often considered one of the greatest commanders in history, his wars and campaigns are studied at military schools worldwide. He also remains one of the most celebrated and controversial political figures in Western history. Napoleon had an extensive and powerful impact on the modern world, bringing liberal reforms to the numerous territories that he conquered and controlled, especially the Low Countries, Switzerland, and large parts of modern Italy and Germany. He implemented fundamental liberal policies in France and throughout Western Europe. His lasting legal achievement, the Napoleonic Code, has been adopted in various forms by a quarter of the world's legal systems, from Japan to Quebec.

Napoleon was born in Corsica to a relatively modest family of noble Tuscan ancestry. Napoleon supported the French Revolution from the outset in 1789 while serving in the French army, and he tried to spread its ideals to Corsica but was banished from the island in 1793. Two years later, he saved the French government from collapse by firing on the Parisian mobs with cannons. The Directory rewarded Napoleon by giving him command of the Army of Italy at age 26, when he began his first military campaign against the Austrians and their Italian allies, scoring a series of decisive victories that made him famous all across Europe. He followed the defeat of the Allies in Europe by commanding a military expedition to Egypt in 1798, invading and occupying the Ottoman province after defeating the Mamelukes and launching modern Egyptology through the discoveries made by his army.

After returning from Egypt, Napoleon engineered a coup in November 1799 and became First Consul of the Republic. Another victory over the Austrians at the Battle of Marengo in 1800 secured his political power. With the Concordat of 1801, Napoleon restored the religious privileges of the Catholic Church while keeping the lands seized by the Revolution. The state continued to nominate the bishops and to control church finances. He extended his political control over France until the Senate declared him Emperor of the French in 1804, launching the French Empire. Intractable differences with the British meant that the French were facing a Third Coalition by 1805. Napoleon shattered this coalition with decisive victories in the Ulm Campaign and a historic triumph at the Battle of Austerlitz, which led to the elimination of the Holy Roman Empire. In October 1805, however, a Franco-Spanish fleet was destroyed at the Battle of Trafalgar, allowing Britain to impose a naval blockade of the French coasts. In retaliation, Napoleon established the Continental System in 1806 to cut off continental trade with Britain. The Fourth Coalition took up arms against him the same year because Prussia became worried about growing French influence on the continent. Napoleon knocked out Prussia at the battles of Jena and Auerstedt, then turned his attention towards the Russians and annihilated them in June 1807 at Friedland, which forced the Russians to accept the Treaties of Tilsit.

Hoping to extend the Continental System, Napoleon invaded Iberia and declared his brother Joseph the King of Spain in 1808. The Spanish and the Portuguese revolted with British support. The Peninsular War lasted six years, noted for its brutal guerrilla warfare, and culminated in an Allied victory. Fighting also erupted in Central Europe, as the Austrians launched another attack against the French in 1809. Napoleon defeated them at the Battle of Wagram, dissolving the Fifth Coalition formed against France. By 1811, Napoleon ruled over 70 million people across an empire that had domination in Europe, which had not witnessed this level of political consolidation since the days of the Roman Empire. He maintained his strategic status through a series of alliances and family appointments. He created a new aristocracy in France while allowing the return of nobles who had been forced into exile by the Revolution.

Tensions over rising Polish nationalism and the economic effects of the Continental System led to renewed confrontation with Russia. To enforce his blockade, Napoleon launched an invasion of Russia in the summer of 1812. The resulting campaign witnessed the catastrophic collapse of the Grand Army, forcing the French to retreat, as well as leading to the widespread destruction of Russian lands and cities. In 1813, Prussia and Austria joined Russian forces in a Sixth Coalition against France. A chaotic military campaign in Central Europe eventually culminated in a large Allied army defeating Napoleon at the Battle of Leipzig in October. The next year, the Allies invaded France and captured Paris, forcing Napoleon to abdicate in April 1814. He was exiled to the island of Elba. The Bourbons were restored to power and the French lost most of the territories that they had conquered since the Revolution. However, Napoleon escaped from Elba in February 1815 and took control of the government once again. The Allies responded by forming a Seventh Coalition, which ultimately defeated Napoleon at the Battle of Waterloo in June. The Royal Navy then thwarted his planned escape to the United States in July, so he surrendered to the British after running out of other options. The British exiled him to the remote island of Saint Helena in the South Atlantic. His death in 1821 at the age of 51 was received with shock and grief throughout Europe. In 1840, a million people witnessed his remains returning to Paris, where they still reside at Les Invalides.

Hey (:

## #16 Re: Help Me ! » Movement of flea » 2016-05-07 05:15:31

Agreed. Or... it refers to displacement and the minimum is 60 metres while the maximum is the highest speed the flea can achieve while changing direction.

## #17 Re: Help Me ! » Movement of flea » 2016-05-07 00:27:23

Hi thickhead, I think you missed that the flea was observed for 60 minutes, not 60 seconds. Besides that, you and I agree with bobbym, and I like the tricky second interpretation you mention

I think there must be another interpretation, however. The distinction between distance and displacement would only be useful if the flea moved in multiple directions. So the 1-metre movement observed by each student must refer to displacement, while the question refers to distance. The problem seems a bit silly then though... mustn't the maximum then be merely the maximum speed per hour the flea can achieve whilst changing direction rapidly?

## #18 Re: Puzzles and Games » Weather forecast » 2016-05-06 04:55:10

Hi salem_ohio

You are right about the four cases and you understand the method But I agree with thickhead that you happened to put the wrong fractions of station B's probabilities: The denominator is 10. When you fix that, you get:
1) 18/25
2) 1/50
3) 2/25
4) 9/50

And also:
A) 4/13
B) 9/13

What you calculated, which happened to result in a 1/3:2/3 split, was for:
-Station A is right 80%, but
-Station B is right 88.8888...%

## #20 Re: Puzzles and Games » Weather forecast » 2016-05-05 05:45:46

Hey bobbym (:

We must eliminate the apparent chance they are both right or both wrong (25% each for total of 50%). Then:

## #21 Re: Help Me ! » correct formula » 2016-05-05 04:25:23

Oh my god... The 'correct' solution is a picture of some excel cells exactly as given in post #25. And when oranghijau posted your answer.... which, by a stroke of luck, exactly corresponds to the products in those cells expanded to addition/subtraction... it is greeted with scrutiny, the admonition to not overcomplicate things and keep it simple stupid, a restatement of the now unmasked rubbish condition to only use the digits once (which is based on lacking the imagination to convert between addition and multiplication), and the final admission that even though the answer differs from the original one (which, even if that were an excuse, is totally false), it appears to work

## #22 Re: Help Me ! » correct formula » 2016-05-05 04:03:37

Sorry, 837. That should be the number of valid solutions with the first digit multiplied only by 1 (I forgot) and the others multiplied by positive integers from 1 to 10. Infinite solutions are for when you extend to any coefficients satisfying post #3's terms. And that's just a small part of the range of answers with very restricted boundaries, within one fixed application of operations (multiplying by coefficients and summing).

Cannot speak for answers with no repetition or reordering and +,*,() only, though.

## #23 Re: Help Me ! » correct formula » 2016-05-05 03:41:28

Also, how is it any more valid a solution than the original one of post #2...

Just generated 835 more such formulas in addition to the 2 we stated in excel in the hopes of finding something easy to convert to a form with "no repetition", as well. I don't know what's more painful; the problem, or the comprehension skills of those promoting it.

## #24 Re: Help Me ! » correct formula » 2016-05-05 01:25:48

phrontister wrote:

You'll find that the answers I posted are correct.

I concur However, there are infinitely many correct solutions of a similar type.

## #25 Re: Puzzles and Games » Weather forecast » 2016-05-04 23:53:42

Hi Typically, to find the chance of two random events both occurring, multiply the probabilities. In this case, however, they cannot both be right (.8*.9=.72) or both be wrong (.2*.1=.02). So we have to eliminate this artificial 74% to get probabilities out of the remaining 0.26 instead of 1.

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