Solution to prize problem listed on page 29 of THE MATHEMATICS CALENDAR 2011 was given by David Johnson on Jaunuary 1, 2011.

Johnson presented both of these correct solutions: (1+1+1+1)!! = (4)!! = 4 x 2 =8 and 111two +1 = 4+2+1 +1 =8

It is fascinating to see how many different solutions have been created for this problem. Below are those submitted since Johnson's solution.

On September 1, 2011, David McKenna sent the following solution: ( (1+1)*arccos(-1))/arctan(1) =8

On September 9, 2011, Marc Strauss sent the solution: 8 = 1/.1 - 1 - 1


Book & Calendar Corrections

List of typos, omissions, proofing errors for:


Do the math!

page 152: The number, "34.75", shown in the second line from the bottom should be "34.25".

page 175: The sequence "3 ,0 ,2, 9, 7, 3 ,0 ,2, 9, 7, 3, ...", shown should read "3 ,0 ,0, 9, 7, 3 ,0 ,0, 9, 7, 3, ...".



January's topic page 5th line of last paragraph replace "questionaire's" with "questioner's"

January 4: First equation should read 0.5-7y=13

January 24: The word "polygon" should be "polygons".

January 27: Problem should have a "-1" after the "+1".

February's topic page last paragraph should begin with "Sallow's discovery ushered . . ."

June 14: The equation should read as follows:(2x-7)(4x^2 + ?x + 49) = 8x^3 - 343

June 25: Note that both the cyclinder and the prism are the same height. The aluminum sheet is to be a rectangle.

August 14: Replace "f(g(x))=?" with f(g(3))=?".

August 24: The diagram is not drawn to scale.

September 20: Replace the word "trajectile" with "trajectory".

September's solution page for BRAIN BUSTERS: For the " four nickle problem" the answer for the area of the red circle is (3r^2 - 2r^2 (square rooot of 2)) pi.

October 18: The fraction bar was left off the problem. The problem should read (5-2i)/4+i.

December 16: Add the phrase "x is a rational number".

December's topic page: Correct the spelling for "Lobachevsky".




January 25: Spelling is "googolplex" not "googolpex"

March10: Spelling is "sweep" not "sweap".

March 11: |AC| should be given as 44 / (square root of 7).

May 13: The problem should read: and x does not equal 0.

June 5: The equation should be:

September "The novel Problem" The total number of digits, as indicated in the solution section, is suppose to be 2553 not 2443.



February 16: Set A should read: A={factors of 96 greater than 6}.

September 7th: The sequence should read: 7^1, 7^2, 7^3, 7^4,...,7^n,...

September's solution at the back of the calendar for the "Which is larger?" brain exercise omitted the coefficients for the expansion of 9^8 when expressed as (1+8)^8. These coefficients are shown below in bold type.

It should read: 9^8=(1+8)^8 = 1(1^8) =8(1^7)8+28(1^6)8^2 + 56(1^5)8^3 + 70(1^4)8^4 +56(1^3)8^5 +28(1^2)8^6 +7(1^1)+8(1)8^7 +1(8^8) which simplifies to 1 + 8^2 + 28(8^2) + 56(8^3) + 70(8^4) +56(8^5) + 28(8^6) + +8^7 + 8^8. Comparing these terms to the eight corresponding terms of 8^9 which are 8^8+8^8+8^8+8^8+8^8+8^8+8^8+8^8, we can deduce that 8^9 is larger.than 9^8.

The solution for brain exercises "Flipping the pennies problem" was accidently not included. THE ANSWER for the millionth coin is T.

EXPLANATION: H stands for Heads and T for Tails. Make a list of how the first 17 coins will end up. Study the pattern of H and s associated with each coin's number. You will notice a coin starting out as a H will return to a H if it is flipped twice, or flipped any even number of times. If we can determine if a coin's number will flip it an even or odd number of times, we can determine if the millionth or any other coin will be a H or a T. The answers lies in determining the distinct number of factors of the coin's number. If this number has an even number of distinct factors it will end up being a H, and if it has an odd number of distict factors it will end up being T. Now look at all the coin's in your list that are associated with perfect square numbers. Note that these are always T. Looking at the distinct factors of perfect squares, we realize they will always have an odd number of distinct factors. Any coin on a perfect square will have an odd number of distinct factors which results in its last flip being a T. In fact, closer inspection shows that only coins with perfect square numbers have an odd number of distinct factors because it's perfect square means one of its factors is repeated and therefore excluded from the listing of distinct factors. For example, 25 has factors (1,25);(5,5), so we have to eliminate one of the 5 factors. All coin numbers, other than perfect squares, will have an even number of factors none of their factors are duplicated, and therefore are not eliminated. The millionth coin's number— 1,000,000— is on a perfect square, (1000)^2. Thus it has an odd number of distinct factors making its final flip a T.

October 4th: Problem should read: "To the nearest mile, how far does the tip of the 1/2" second hand travel in 60 days?"


THE ADVENTURES OF PENROSE -Copyrght 1997, First Edition

PAGE 56- The second column, fifth line down should read: "(1/1,000,000,000) the size of the cat"



February 15: The denominator marks were left off. The line about h1 and h2 should read h1 / h2 = 3 / 4.

February 20: The "0" numeral in the ones place for the date, February 20, did not print .

March 4: The "1" numeral appearing on the date should be 4, so that the date reads March 4 rather than March 1.

May 2: The expression should read (6-2[3m+4(2m-1)]) / 7-11m

May 15: The equation should read [(7.2 x 10^3) (1.4 x 10^6)^2] / 10   =  1.4112 x 10^?

May 27: The expression should read the 5th route of 9 to the 3rd power times the 5th root of 3 to the square root of 81, rather than the 3rd root of 3 to the square root of 81.

June 26: The Chinese number is supposed to be subtracted from the Babylonian number.

July 20: Replace diagram with the following:

October 27: The expression should read 1+2+3+...+25+26+27+26+25+...+3+2+1 = ?^2



June: In the beginning of the 4th paragraph: "Charles Babbage (aka Lewis Carroll)" should read "Charles Dodgson (aka Lewis Carroll)".


January 28:
The graph should show the area bounded by the parabola and the lines x=, x=2, and y=0.

July 5: Replace "-?" by "?".
September 26: Replace (15-3i)/? with (15+3i)/? .
MATHEMATICAL SNIPPETS -Copyrght 2008, First Edition, First Printing June 2008.
PAGE 42- The formula for "p" in the 5th line from the bottom of the second column should read "p is of the form 2^(2^n) + 1..." .
PAGE 43- The fourth line of the first column should read "Using Gauss' formula, p =2^(2^n ) + 1..."
PAGE 161- The italics in the 2nd column first paragraph should read another, and are stitched together by mathematics."
PAGE 162- In the 2nd column first paragraph the word "hallow "should be "hollow".
PAGE 171- The first column 6th line should read "of 144, namely 1/48, 1/24, 1/16, 1/12, 7/48, and 1/6."
January 17:
The problem should read: "...then its range consists of natural numbers greater than or equal to ? ."

November 24: The problem should read: "B's Ice Cream parlor offers 3 different flavors... ?"



April 30: Delete the value 120 from side AB.

May 14: The problem should read: Determine the maximum y-coordinate where this curve's tangent is zero.



January 5: Option (5) should read: 5) No rectangles are trapezoids.

March 30: The problem should read: x is a rational number.  What must x equal for this triplet to represent the sides of a right triangle.

Dec 6: The following equation is missing: 4x^2 +20x + 4y^2 ­ 48y = -165

Footnote 8 for BRANES ON THE BRAIN­The big tests at CERN are coming should read "8The Large Hadron Collider(LHC) is the newest addition to CERN. Its 27km circumference makes it the world's largest superconductivity installation. Superconductivity allows certain materials to conduct electricity without the loss of energy. This usually takes place at extremely low temperatures. LHD is located at at average depth of 100m underground and will operate at around 300° below room temperature, which is colder than outer space. LHD now occupies the 27 km circle which had been where the earlier LEP collider was located."



page 63- The number in the square that appears at the intersection of the 4th column and 3rd row should be 12.

page 159- Correct a typo in the DAY NUMBERS chart, the number corresponding to  Saturday's should be 0, not 7.

Revise the steps as follows for example August 27, 1990.
1) Take the last two figures in the year, 90.  This number will be used in both step 2 and 5.
2) Divided the 2-digit number from step 1 by the number 4, and ignore its remainder. 90÷4= 22 (and the remainder 2 you ignore).
3) Go to the month chart and find the month's number. It is 3.
4) From the desired date, take the day's number. For our example date it is 27.
5) From the century chart find the century number for the desired year. For 1990 its is 0.
6) Now, add together the numbers from steps 1, 2, 3, 4,5.  

Divide this sum by 7, namely 90+22+3+27+0 = 142 So, 142÷7  = 20 plus remainder 2.

Use the remainder number to look up the day of the week in the DAY NUMBERS chart. For 2 it is Wednesday.



3rd printing May 2004

page 217- solution for FEB 18's last sentence should read " n(n - 3)/2 = 65 --> n =13. So the polygon has 13 sides."

page 209- Dec. 25th's problem diagram should show a 4" by 9" rectangle rather than a 4" by 6".

page 218- Mar. 6th's solution should read: "The pips on the opposite faces of a die always total 7. The pips on a die total 21. Since there are 7 dice pictured on page 39 (March 6th problem), the total number of pips on the 7 dice is 7x21=147. Of these, 46 are visible, so those hidden are 101 pips = 147-46 ."

page 226- June 26's solution: The second line show the square root bar extending over (3x4), which makes the answer: 44 - 8 sqrt3 .



January 19: Should read:  F+4   This hexadecimal sum is ___in base ten."

April 28: Should read:  " A stone-like object dropped in 8 feet of water in a cylindrical vat with a 4' diameter floats in the vat. The stone-like object raised the water level to 0.43 inches. Water weighs about 62.205 lbs per cubic foot. What is the stone-like object s weight to the nearest pound?"

May 21: 3(square root of 2) should read 7(square root of 2):  The statement should read: "(9/49) of this cone's volume is ___pi cubic units."

June - In topic, replace the phrase "3.415926... its symbol" with "3.1415926... its symbol" . In June's footnote at back of calendar The golden mean should read "1.6180339887...".

September 10: Should read:  50! ends in 2+__zeros."

December 23-: The angles in the diagams should be changed as follows: 70 degrees is a degrees. 110 degrees should be 180 degrees minus a degrees.

December 30: The first sentence should read: "Two friends flew with 105 lbs. of baggage together.".



January 4- The word "thousands" in the last sentence should be "hundreds".
January 16- The last sentence should read "Its volume is ___(sq. root of 2)/3."

April 2- The number 6 in the equation should be a negative 6.
April's story-The 2nd to the last sentence should read "In fact, a square is a convex quadrilateral."

May 10-The questions should read: "Find the radius of the circle."

June 20- The point of tangency on the side of length 4 is also a bisection point. Two marks on each side of this tangent point were left off.

July 16- The 40° should be deleted

July 30- After the last 15 in the problem, the square root of 2 should follow it, so it reads: 15(square root of2)

August 9-- The final sentence should read: "Find the largest value for its width."

Page 26 under FOOTNOTES & ADDITIONAL INFORMATION: In footnote 8 delete ".com" after the word "Hotbits".