







Counting in base five using words not digits 
20140125 

From Randy: We all know how to count (in the base 10/decimal system) using words not numbers. For example: one, two, three, four, five, six, seven, eight, etc. However, in base 5 (for example) how would you count (in words). For sure  in base 5 the number 1 could be "one", the number 2 could be "two". However there seems to be no words to describe base 5 numbers beyond 0,1,2,3 and 4 (and perhaps 10). In base 5 the number 10 is not ten. Rather it is "five". In base 5 what word(s) describe numbers larger than 10? What words are used for 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 44,...etc. Also, consider a man and woman were married in the Gregorian year 1964. If they had an anniversary tomorrow  how long would you say they've been married in base 5 speak? In numbers their Golden Anniversary would note 200 years of marriage in base 5. How would you articulate their years together in base 5? I don't recall seeing verbiage to represent numbers in any system other than the decimal/base 10 system. Do such things exist for other systems? Answered by Harley Weston. 





Multiplication in base two 
20130201 

From Michael: multiply in the indicated base
110two*11two Answered by Penny Nom. 





A log base 2 problem 
20081126 

From dave: solve for x
(log base 2 of x)  (log base 2 of (x2)) = 3 Answered by Penny Nom. 





Bags of pennies 
20081011 

From paul: jenny divided 15 pennies among 4 money bags.she could then pay any amount from 1p to 15p just by giving bags.how many pennies did jenny put in each bag? Answered by Penny Nom and Victoria West. 





Aboriginal number groupings 
20080904 

From Barbara: Our current place value system is based on the notion of 10s. Did Aborginal people use a similar system or did they group numbers differently? Answered by Harley Weston. 





Four weights 
20080825 

From Darla: A balance had known weights of 1/2 lb, 1/4 lb, 1/8 lb, and 1 oz. Edna's object weighted 2 oz. more than Paul's. Each used 3 known weights to weight his or her object. which know weights did each use? Answered by Penny Nom. 





Paying with silver  Part 2 
20071017 

From Shanna: The paying with silver problem. I understand how to do the problem, but could you please explain how you would use base 2 arithmetic to solve it. Answered by Penny Nom. 





Log base 2 of log base 2 of x 
20070627 

From alex: y = log base 2 of lag base 2 of x
The slope of the tangent to the given curve at its xintercept is..? Answered by Harley Weston. 





A problem involving logs 
20061126 

From Beth: any help would be appreciated on how to solve without using the change of base formula for logarithms in the solution and check of the solution!!!
log256 (x) + log16 (x) + log4 (x) + log 2 (x) = 7/4 Answered by Stephen La Rocque and Penny Nom. 





cos x * cos 2x * cos 4x * cos 8x 
20050829 

From Leandro:
A = cos x * cos 2x * cos 4x * cos 8x
What's the value of log A at base 2?
Answered by Chris Fisher and Penny Nom. 





1 + 1 = 10 
20030917 

From David: could you please explain to me how 1+1=10 thanks Answered by Penny Nom. 





Papy's Computer 
20020111 

From MaryAnne: My secondgrade son brought home a fun math worksheet which involved calculating sums using "Papy's Computer." I had never heard of this before and found it to be quite interesting. Each digit in a decimal number is represented by a 2x2 grid. Each grid square corresponds to one of the numbers 1,2,4, or 8. Answered by Harley Weston. 





Paying with silver 
20000426 

From Luther Jackson: A silver prospector is unable to pay his March rent in advance. He owned a bar of pure silver, 31 inches long, so he made the following arrangement with his landlady. He would cut the bar, he said into smaller pieces. On the first day of March he would give her and inch of the bar, and on each succeeding day he would add another inch to her amount of silver. She would keep this silver as security. At the end of the month, when the prospector expected to be able to pay his rent in full, she would return the pieces to him. . . . Answered by Claude Tardif and Penny Nom. 

