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 STEVE HAS A BACHELOR OF SCIENCE DEGREE FROM THE UNIVERSITY OF BRITISH COLUMBIA AND HAS BEEN TUTORING MATHEMATICS IN VANCOUVER FOR MORE THAN TWENTY YEARS. HIS ACADEMIC BACKGROUND WAS FOCUSED ON MATHEMATICS AND HE GRADUATED WITH IT AS A MAJOR. STEVE IS ALSO A RECREATIONAL SOFTWARE DEVELOPER AND HAS TEACHING EXPERIENCE GAINED IN ASIA - KOREA, TAIWAN, AND CHINA.

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 THE MATHEMATICAL CALENDAR CONSIDER ANY DATE AFTER 1582 (ADOPTION OF GREGORIAN CALENDAR) LET : N=DAY OF THE MONTH, M=MONTH NUMBER (starting with march=1), C=HUNDREDS PART OF THE YEAR, Y=OTHER PART OF THE YEAR, L=1 IF LEAP YR, 0 OTHERWISE, [X]=GREATEST INTEGER LESS THAN OR EQUAL TO X. THEN THE WEEK DAY IS : d = N+[2.6M-0.2]+Y+[Y/4]+[C/4]-2C-(1+L)[M/11] (mod7) (Sunday = 0, Monday =1, etc) ( mod 7 = remainder when divided by 7 ) EXAMPLE : Oct 18 1998 N=18, M=8, C=19, Y=98, L=0 d = N+[2.6M-0.2]+Y+[Y/4]+[C/4]-2C-(1+L)[M/11] (mod 7) d = 18+[20.6]+98+[98/4]+[19/4]-38-(1)[8/11] (mod 7) d = 18+20+98+24+4-38-0 (mod 7) d = 126 (mod 7) d = 0 ------> Sunday THE MISSING DOLLAR PROBLEM Three people have dined at a restaurant and received a total bill for \$30. They agree to split the amount equally and pay \$10 each. The waiter hands the bill and the \$30 to the manager, who realizes there's been a mistake and the correct charge should be only \$25. He gives the waiter five \$1 bills to return to the customers, with the restaurant's apologies. However, the waiter is dishonest. He pockets \$2, and gives back only \$3 to the customers. So, each of the three customers has paid \$9 and the waiter has stolen \$2 making a total of \$29. But the original bill was for \$30. Where is the missing dollar ? PROOF THAT n = n + 1 A LIMERICK A dozen, a gross, and a score Plus three times the square root of four Divided by seven Plus five times eleven Is nine squared and not a bit more. ARISTOTLE'S WHEEL PARADOX THE OUTER CIRCLE TURNS ONCE WHEN GOING FROM A TO B, AS DOES THE INNER CIRCLE WHEN GOING FROM C TO D. HOW CAN THIS BE?   AB IS THE SAME LENGTH AS CD, BUT THE CIRCLES ARE A DIFFERENT SIZE. BENFORD'S LAW If a number is chosen at random from a large table of data or statistics, the chance that the first digit is 1 is about 30.1%, that the first digit is 2 is about  17.6%, that it is three is 12.4%, . . . . . , that  it is 9 is 4.5%.  In fact, the probability the first digit is d is log(1+1/d). Benford tested thousands of different collections of data, including the surface area of 335 rivers, specific heats and molecular weights of thousands of chemicals, baseball statistics,  and addresses chosen at random. HAM SANDWICH THEOREM Given a sandwich in which bread, ham, and cheese (three finite volumes) are mixed up, in any way at all, there is always a flat slice of a knife (a plane) that bisects each of the ham, bread, and cheese. In other words, however messed up the sandwich – even if it's been in a blender – you can always slice through it in such a way that the two halves have exactly equal amounts, by volume, of the three ingredients. THE MONTY HALL PROBLEM Pick a door. Behind one of them is a NEW SAIL BOAT, and behind the other two are goats.  The Monty hall problem as explained by Stedwick . NOTES

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