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January 21, 2017
Posted by **Josh** on Monday, February 21, 2011 at 9:44pm.

2) If you take any valid time from a 12 hour clock, what is the maximum sum you can obtain by adding the digits? (Eg. For 7:14, the sum is 7+1+4=12)

THANKS!

- Math Trivia -
**Ms. Sue**, Monday, February 21, 2011 at 9:47pm2)

Isn't it 12:59? - Math Trivia -
**Josh**, Monday, February 21, 2011 at 10:05pmyah thanks!

i am having a hard time with number one. i know i could sit down and take a long time to do it...but i was wondering if their was a formula to it, or a quicker way to do it... - Math Trivia -
**Reiny**, Monday, February 21, 2011 at 10:13pmmake a list of lockers up to whatever you feel like

put c for closed under each one

starting with 2,4,6,8,...switch the c to o, for open

starting with 3,6,9,12,.. switch to c's to o's, and the o's to c's

starting with 4,8,12,16,... switch the c's to o's, and the o's to c's

continue....

you will notice that only the perfect square numbers will be c's

so which are the perfect squares ?

1,4,9,16,25,36,49,64,81,and 100

somebody actually spent time and effort to create an applet that shows this pattern.

only in this problem the first student starts by switching all the lockers, so in their case all the lockers are initially open.

(For some reason on my computer it seems to jump to the final stage almost right away)

(Broken Link Removed) - Math Trivia -
**MattsRiceBowl**, Monday, February 21, 2011 at 10:38pmI don't know how to do number 1 since it doesn't say how many lockers there are initially. It says "1--," but not sure if that should be something else.

- Math Trivia -
**MathMate**, Monday, February 21, 2011 at 10:43pmQuestion 1

This has to do with the number of factor of an integer. An even number of factors will cause the door to be toggled (open/close) an even number of times, therefore they will remain closed.

For example, a prime number has two factors:

7=(1,7), 13=(1,13).

Almost all other numbers have an even number of factors:

24=(1,2,3,4,6,8,12,24),

88=(1,2,4,8,11,22,44,88)

You will notice that the product of the first and the last factors give the number itself.

Since the factors are always different, there is an even number of them... except in the case of perfect squares, where the middle factors are identical, so we count them only once, and the locker will be visited an odd number of times, leaving them open.

Examples:

9=(1,3,9)

81=(1,3,9,27,81)

100=(1,2,5,10,20,50,100), etc.

Question 2:

If we were to add all digits separately, I would suggest 9:59 which gives a sum of 23 as the highest sum. - Math Trivia -
**Ms. Sue**, Monday, February 21, 2011 at 10:53pmMathMate is obviously correct. 9:59 yields a greater sum than 12:59.