# Oct 2017 (CML)

I will post seven new problems every weekend.  If you like you can try to finish the first 6 problems in 30 minutes, just like in a typical CML test.  The 7th problem is a bonus. The idea is that you work on your own during the week and I will post answers the following Saturday.  For those of you who practiced with me last year, the process is similar.

For instructions on submitting weekly answers, click on the “Logistics” tab.
For previously posted problems, click on the “Archive” tab.
For previous prizes, click on the “News” tab.

This week we work on Halloween cookies and candies 🙂

Week of Oct 29 – Nov 4.

Oct 29: Sam needs 15 dozen Halloween cupcakes. He bakes 2 dozen on the first day, 4 dozen the second day, 6 dozen the third day, and the pattern continues.  Every day half of the cupcakes are eaten by his friends.  How many days does Sam need to get his 15 dozen cupcakes?

Answer: 5.  Sam has 1 dozen, 2 dozen, 3 dozen, etc left every day.  So he needs 5 days to get to 15 dozen.

Oct 30: At a business meeting right before a Halloween party, every 10 minutes half of the remaining people left the meting.  After 1 hour, the next-to-last person left the meeting. How many people were at the beginning of the meeting if nobody entered the meeting?

Answer: 64.  After 60 min, 1 person left and 1 person remained.  After 50 min, 2 people left and 2 people remained. … After 10 min, 32 people left and 32 people remained.

Oct 31: At a Halloween party, there are 4 times as many witches as ghosts. When 9 witches leave, there are 3 times as many witches as ghosts. How many witches are there at the party initially?

Nov 1: A has more Halloween candies than B and C combined. B has exactly twice as many candies as C. C has more candies than D. A has exactly 4 times as many candies as D. None have more than 19 candies. How many candies does B have?

Nov 2: Lisa gave away 1/6 of her Halloween candies on Nov 1, gave away 1/5 of the remaining candies on Nov 2, and gave away 1/4 of the remaining candies on Nov 3.  On Nov 4, she had 24 candies left and she kept them to herself.  How many candies did she give away?

Answer: 24.  On Nov 3, Lisa gave away 8 since the remaining 24 was 3/4. On Nov 2, Lisa also gave away 8 since the remaining 32 was 4/5.  On Nov 1, she gave away 8, since the remaining 40 was 5/6.

Nov 3: A gave 10 of her 25 candies to B and now B has twice as many candies as A.  How many candies do A and B have in total?

Nov 4:  A costume and a bag of candies cost \$42 in total before Halloween. After Halloween, the costume went on sale for 50% off, and the candy bag went on sale for 75% off.  Now the costume and the bag of candies cost \$18 in total.  How much was the costume before Halloween?

This week we focus on problems related to coins .

Week of Oct 22-28.

Oct 22: A dollar bill is exchanged for 9 coins. Using only quarters, dimes and nickels, how many nickels will be used if more dimes are used than nickels?

Answer: 1 nickel (1Q, 7D, 1N)

Oct 23: Six pieces of candy were paid for with 1 quarter, 2 dimes, 3 nickels and 4 pennies. Nine pieces of candies should be paid for with 2 quarters, 2 dimes, 2 nickels and ___ pennies.

Oct 24: Peter has 3 times as much money as Tom. Tom has 3 dimes and 2 nickels. Peter has the same number of quarters as nickels, and he has no other coins.  How many coins does Peter have?

Oct 25: Rachel has 1 quarter, 1 dime, 1 nickel and 1 penny. Using at least 1 out of the 4 coins, how many different amount of money can Rachel make?

Oct 26: Rachel has 1 quarter, 1 dime and 2 nickels. Using at least 1 out of the 4 coins, how many different amount of money can Rachel make?

Answer: 9 (5, 10, 15, 20, 25, 30, 35, 40, 45 cents)

Oct 27: Mr. L has 5 nickels and 5 dimes to be divided among his 3 kids, A, B and C, so that each child has the same amount of money.  A gets the most number of nickels.  A gets ___ dimes and ___ nickels, B gets ___ dimes and ___ nickels, and C gets ___ dimes and nickels.

Answer: A: 1D, 3N, B: 2D, 1N, C: 2D, 1N

Oct 28: Using pennies, nickels, dimes and quarters only, what is the minimum number of coins needed to cover every choice of \$0.05, \$0.15, \$0.25, \$0.35, \$0.45, \$0.55, \$0.65, \$0.75, \$0.85 and \$0.95?

This week we focus on problems related to integers.

Week of Oct 15-21.

Oct 15: If the units digit and the hundreds digit of the number 428 are switched, what is the sum of the original number and the new number?

Oct 16: What is the largest 5-digit number in which the digit in the thousands place is three times the digit in the tens place?

Oct 17: A 2-digit number A is less than 50. When A is put in groups of 7, then 3 is left. What is the largest possible sum of the two digits of A?

Oct 18: If you use 6 digits 1, 2, 3, 4, 5 and 6 each exactly once to form two 3-digit numbers, what is the largest sum of the two numbers?

Oct 19: If you use 7 digits 1, 2, 3, 4, 5, 6 and 7 each exactly once to form one 3-digit number and one 4-digit number, what is the difference between the smallest 4-digit number and the largest 3-digit number?

Oct 20: Leo made a mistake in his calculation. He was supposed to divide by 4, but instead he multiplied by 4. He got 1024 as the answer. What is the correct answer?

Oct 21: The reversal of a number reverses the ordering of the digits. For example, the reversal of 213 is 312.  Add 627 to its reversal, and call this sum A. Subtract A from the reversal of A. Call this difference B. Add B to its reversal. What is the answer?

This week we focus on calculating rates and speeds.

Week of Oct 8 – Oct 14, 2017

Oct 8: Diego lives 2 miles from school. If he walks a mile in 17 minutes and school starts at 7:55am, when should Diego leave his home?

Oct 9: A pond is 12.34 feet deep at the beginning of the year. The annual rainfall is 1.5 feet and the annual evaporation is 0.8 feet.  The pond at the end of the year is ____ feet deep.

Oct 10: A blizzard lasted from 11pm to 5am the next morning. Two and half inches of snow fell every 45 minutes. How deep was the snow at 5am?

Oct 11: Robert is reading a 242-page book. He reads 11 pages every 15 minutes and he takes a 5 minute break every 30 minutes.  Robert starts reading at 9am.  When will he finish the book?

Oct 12: Al gave Bobby a 20-yard head-start in a race. Al ran 3 yards per second and Bobby ran 2.5 yards per second. How many seconds did it take Al to catch up with Bobby?

Oct 13: Al gave Bobby a 10-yard head-start in a race. Al ran 3 yards per second and Bobby ran 2.75 yards per second. How many yards did Al run when he caught up with Bobby?

Oct 14: 40 workers can build 40 boats in 4 days. How many days would it take 10 workers to build 10 boats?

This week we focus on problems related to dates and days of the week.

Week of Oct 1 – Oct 7, 2017

Oct 1: Mrs. A works five days a week, Monday through Friday. If there are no holidays in a 30-day month, she can work as many as ___ days or as few as ___ days.

Oct 2: Stephanie was born on a Tuesday, June 27.  If Emily was born on Aug 13 of the same year, what day of the week was Emily born?

Oct 3: In a 366-day calendar year, there are ___ more odd-numbered days than even-numbered days.

Oct 4: In July of any year, the fourth Sunday of the month is anywhere from July ___ to July ___.