1. What can you hold in your left hand, but not your right hand? (Multiple answers?)
2. In the US, 5/2 means May 2, but in England it means Feb 5 (they put the day first). How many days each year have the same abbreviations in both countries?
3. What is the next combination of letters and numbers in this pattern? A1Z26, B3Y24, C5X22, ____
4. Find the smallest of 5 consecutive integers whose sum is 100.
5. Find any value of t that makes 19/t + 5/t a whole number. (Mini Bonus: Can you find all values of t that work?)
6. At what time is the sum of the digits on a digital clock the greatest?
7. The transistor was invented in a year close to the middle of the 20th century. The tens’ digit of the year is 4 times the thousands’ digit and one-half of the ones’ digit. In what year was it invented?
8. Two 5 x 5 squares overlap to form a 5 x 7 rectangle. What is the area of the region in which the two squares overlap?
9. What fraction of the small squares on a chessboard are covered (occupied) by playing pieces at the start of the game?
10. Eric’s school system has 9000 pupils and a teacher-pupil ratio of 1:30. They feel this is too high, and want to reduce it to 1:25. How many more or fewer teachers are needed to achieve this goal?
Exploration/Mini Research? We have another 5-Monday-month this month – and it’s February!! This has got to be rare! It has to be leap year to have 5 of any day in February, but Mondays? HOW RARE IS THIS?
(I only know this answer vaguely, and I don’t think it’s exact. I suspect I’m just wanting someone to Google it for us and fill us in. :-))
10 thoughts on “February ’16 Brain Teasers”
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NOTE: This is a duplicate comment, but I’m re-doing it & tweaking the post time, so it will appear BEFORE the Comments mentioned below :-). Sorry for duplication and/or confusion:
Readers: I’ve gotten some interesting and fascinating comments on the “5th Monday – Leap Year” topic above from Jim Waterman. And I’ve neglected posting them this week.
I was hoping only for someone to look up (too lazy myself) the usual frequency of this event (I THINK it’s 16 – 40 years, depending), but Jim has observed and given MUCH more! 🙂
I’ll go ahead and post them now (someone can still give history/future for us). Hope you’ll enjoy them.
Larry
Exploration/Mini-Research: Leap year. This is not as straight forward as it may seem on first blush because 3 potential leap years are removed within a 400 year period. For the years that are evenly divisible by 100 (the years that end in double zero) but not divisible by 400 are eliminated; the years 1700, 1800, and 1900 were not leap years; the years 2100, 2200, and 2300 will not be leap years. Therefore within any 400 year period there are only 97 leap years, not 100 leap years. Any calculation must consider this fact.
1. There are 5 Mondays (or any other days of the week) in February every 7th leap year. The last year in which there were 5 Mondays in February is 1988.
2. There is an average of 13.85714286 leap years that have 5 Mondays within a 400 year period (97/7=13.85714286).
3. Therefore among leap years the percent of leap years that have 5 Mondays (or any other day of the week) is 14.2857143% (13.85…/97=14.28…).
4. Therefore among all years the percent of years in which there are 5 Mondays in February is 3.4642857% (13.85…/400).
jdw
I went back an calculated our current century with 25 leap years. There will be 3.571428571 5-Monday
Februarys. That makes 14.285% of leap years and 3.571% of all years with 5-Monday Februarys . Hardly any difference with the 400 year calculations.
jdw
What will happen when we get beyond the third 5-Monday February this century when there will be 0.571428571 of a 5-Monday February? : )
Within what time frame is there a whole number of 5-Monday Februarys? I bet Bill Murray knows.
jdw
1. Your right hand.
3.D7W22
4. 18, 19, 20, 21, 22
5. T=2 and 4
1. your left wrist, left forearm, left elbow, or any part of your left arm below the shoulder
2. 12 days – the ones where month=day
3. D7
4. The only ones I found were 18, 19, 20, 21, and 22. But the word “smallest” in the problem makes me think there are other possibilities?
5. Any integer factor of 24 would work (I think) – 1, 2, 3, 4, 6, 8, 12, 24
something has gone awry – when I checked 2104 it should have been a 5-Monday February year, but it is a 5-Friday February year. Likewise 1896 and 1904 are both 5-Monday February years and do not align with the q7 year rotation. So, this is getting much more complicated. There must be a pattern that I do not see yet.
Please keep the calculation for this century (3 5-Monday Februarys), but disregard the 400 year calculation.
jdw
#5 19/t + 5/t = whole number. If t = 1, then 19/1 + 5/1 = 24; if t = 24, then 19/24 + 5/24 = 24/24 = 1.
jdw
#2 Month and Days US and England: there are 12 days of the year that are the same in both US and England; 1/1, 2/2, etc.
#3 Combinations: D7W20
#4 Add up to 100: 18
#6 Digital Clock Sum: 9:59
#7 Transistor Year: 1948
#8 Overlap Area: 3X5
#9 Chess: 32 out of 64 spaces: 1/2
#10 Teacher to Student ratio – at 1:30 there are 9000 and 300 teachers. at 1:25 there will be 9000 and 360 teachers. 60 more teachers are needed.
6. The time is 9:59 which equals 23
7. 1948-if this is right it was TOO easy. 🙂
8. 15 3/8 square inches
9. 1/2
10. They need to add 10 more teachers.