







Seven tangent circles 
20180423 

From Domenick: How to calculate the circumscribed and inscribed circles formed by seven .019685 diameter circles arranged in a circle with all seven circles tangent to each other? Answered by Penny Nom. 





Seven switches with 3 stages each 
20150915 

From jeff: We are trying to solve a combination problem. If I have 7 things that can be in 3 states (say on/partially on/off), and all 7 have to a state. How many different combinations can there be? It doesn't seem like we should treat it as 21 independent things, but not sure how to break the problem apart. Answered by Penny Nom. 





Counting by sevens 
20100413 

From Larry: Lee counted by 7's beginning with one of the whole numbers from 1 through 7, until Lee passed 1000. If Lee counted
three of the following numbers, which number did Lee NOT count?
a. 107
b. 184
c. 534
d. 641
Answered by Robert Dawson and Penny Nom. 





Holiday for 7 golfers 
20100105 

From Andy: I am having difficulty scheduling pairings for a forthcoming Golf holiday. There are 7 players and we will be playing 7 rounds  each round will be a 3 ball and a 4 ball. I am trying to work out a schedule that means everyone plays with each other roughly the same number of times (with a minimum of, say, 3 times if possible). Also, we are looking to ensure everyone plays in roughly the same number of 3 and 4 balls. Any suggestions would be much appreciated (we leave in 10 days time). Thank you. Answered by Victoria West. 





Seven circles 
20090920 

From Bobbi: try to put number 1 to 7 in seven circles (one in the middle, 3 on top, 3 below) so the numbers in each row of three circlesvertical, horizontal, and diagonal  add up to 12. Each number can be used only once. Answered by Stephen La Rocque. 





Ambitious 7th Grader 
20090128 

From John: I have been asked to tutor a 7th grader who is very good in math. He is taking the most advanced course that his school offers to 7th graders. This course will cover Algebra 1 over a period of two years, using McDougal Littell's Algebra, Structure and Method, Book 1, a book I like a lot.
I have been hired not to help him with his schoolwork, which is too easy for him, but to guide him through something in math beyond his schoolwork. This was his idea, an idea which surprised his parents, but one which they support.
Do you have a suggestion for me? If so, I would be very grateful to hear from you. I think this could be a lot of fun for me and my new student, if I pick the right path.
Thanks and best regards,
John
John Answered by Robert Dawson, Victoria West and Walter Whiteley. 





A seven card poker hand 
20090112 

From Sean: from a standard card deck, seven cards are chosen at random.
find the probability that the set chosen contains exactly three of each
of two different face values.
the second part of the problem asks the probability that the card hand contains
exactly three 2's and exactly three 5's. Answered by Robert Dawson. 





A 7digit odd number 
20080626 

From Godryk: I am the smallest 7digit odd number. my ones digit is the sum of my thousands, and ten thousands digits. What number am I? Answered by Penny Nom. 





Base seven 
20070519 

From Dan: A number X is converted to base 7 and becomes a four digit number. Its leftmost digit is removed and written again as the rightmost digit. The number thus obtained is twice X. Find the decimal representations of all such numbers X. Answered by Penny Nom. 





Seven digit account numbers 
20070309 

From Miranda: Account numbers for the Central Oil Company consist of seven digits. If the first digit cannot be 0, how many account numbers are possible? Thank you so much!!! Answered by Penny Nom. 





37 with four 4'2 
20040103 

From Myra: Using four fours and only four fours to get an answer of 37. Answered by Claude Tardif. 





Divisibility by 7 
20031114 

From A student: how do you test a number to see if it is divisible by 7 or not? Answered by Penny Nom. 





Making 7 
20021126 

From Bill: At one time I had the answer to this math equation but I have lost it and can't seem to regain it. I may be going at it wrong but as I recall there were the numbers 1 through 4, and the std operators, +, , /, *, and parentheses. The object was to make the four numbers with the operators equal to 7. Each number and operator may be used only once. My 9 year old loves these quizzes but I can't give it to her if I can't provide the correct answer. Answered by Claude Tardif. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

From Tony: When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Answered by Andrei Volodin and Penny Nom. 





The best of 7 
20010908 

From Michelle: Professional basketball, hockey, and baseball championships are decided on the best 4 out of 7 games. The first team to win four games wins the championship. In how many possible ways could the team win the championship series after winning the first game?
Example:
Game 1 2 3 4 5 6 7
Result W L L W W W
Answered by Leeanne Boehm. 





Generating uniquie 2 digit numbers 
20010716 

From Anthony: What methodology can I use to generate uniquie 2 digit numbers from unique 7 digit numbers. Of'course the total number of 7digit numbers is not greater than 99. Answered by Penny Nom. 





Rule of 78 
20000322 

From Dan Baumgarten: Can you explain the rule of 78 and the reverse rule of 78? Thanks. Answered by Claude Tardif. 

