Last week’s puzzler (divide the clock with two lines so the sums of the numbers in each segment are all equal), is a special case of what might be an interesting math problem: for which positive integers m and n is it possible to divide an m-hour clock with n lines (none of which have 1 through m as…

∀ m>2, ∃ n = FLOOR( (m-1)/2 ) that satisfies your math problem.

As long as there is an even number of integers from 1 to n, there will be pairs of integers whose sum is equal to n+1 (e.g., 12+1, 11+2, 10+3…). So diving them into equal sums becomes trivial. A clock face can be divided into three equal sums or six equal sums.

All the foregoing is much too complicated for me. Maybe it amounts to the same way that I figured it out, but the obsfucation obliterates the similarity. Here’s my take: Given that the sums of the sections must all equal, I thought it prudent to find the outside parameters of those sums. The total …

Obvously, I am not adept at email communications. I don’t even know what I did to get kicked out of the comment box… Moving on: So, the next step would be to find out what the sums of the numbers in each of the sections would be. If there are 4 sections, then each section would have 78/4 as its sum…

mcolvin — VOILA! I thought it was elegant and cool …Cool in mathematics is giving the solution in one short line.

I’ve been following this one because the puzzler is often my favorite part of the show. It seems to me that no one is addressing the OP’s question: is there a generic formulation of and solution to the problem of which the puzzler is a particular instance. ∀ m>2, ∃ n = FLOOR( (m-1)/2 ) just says t…

Why answer the puzzler here? Everyone will see the answer. Or is only the first answer picked?

Because the fun thing is trying to solve the puzzle, not being the one person who wins the $25 prize.

If there is no requirement for the straight lines to run all the way across, you can split into two sections of 39 i.e. Straight line 1: Between 9/10 to the middle Straight line 2: Between 3/4 to the middle Area 1 : 10+11+12+1+2+3 = 39 Area 2: 4+5+6+7+8+9 = 39

@bobs1947 : Or is only the first answer picked. According to the folks at cartalk, a winner is picked at random from among the correct answers received. I would expect instead that entries are picked at random until a correct one is found. Usually, as in this case, the pool of entries was closed a…

Clock puzzler

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littlemouse October 17, 2011, 10:04am 15

Sorry, Mechaniker, “∀ m>2, ∃ n = FLOOR( (m-1)/2 )” still just says “for any number m greater than 2, there is a number n that is less than m”.

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Clock puzzler

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