* 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.

*posted problems, click on the “Archive” tab.*

**For previously****, click on the “News” tab.**

*For previous prizes*~~Click GoogleForm to submit answers by Sat, Feb 3.~~

Week of Jan 28 – Feb 3

Jan 28: A time capsule was sealed in 1940 and will be opened on the same date in 2018. How many years will the capsule remain sealed?

Answer: 78

Jan 29: What is the absolute difference between 1/2 and 1/3 ? Express your answer as a common fraction.

Answer: 1/6

Jan 30: When the integer n is squared, the result is less than 150. What is the sum of all possible values of n?

Answer: 0 (1^2, (-1)^2, 2^2, (-2)^2, 3^2, (-3)^2… 12^2, (-12)^2. So the sum is zero.

Jan 31: Minnie paid a one-time registration fee of $30 for dance lessons. Additionally, she

paid $20 per lesson. If she took seven lessons, how much did she pay altogether?

Answer: 170 = 30+7*20

Feb 1: How many pieces that are exactly 5 inches long can Sue cut from a string that is 7 feet long?

Answer: 16. 7*12/5 = 16.8

Feb 2: How many units away from the origin is the point (−3, −4)?

Answer: 5

Feb 3: In Oregon, which has no sales tax, Gloria bought three notebooks for $1.57 each. If she paid $5.00, what is the least number of U.S. coins that she could get in change?

Answer: 5 coins. 5-1.57*3 = 0.29. 1Q4P

~~Click GoogleForm to submit answers by Sat, Jan 27.~~

Week of Jan 21 – Jan 27

Jan 21: How many 4-digit palindromes contain both the digits 1 and 2?

Answer: 2 (1221, 2112)

Jan 22: What is the radius of a circle with a circumference measuring 24π cm?

Answer: 12cm

Jan 23: On a number line, what number is two-thirds of the distance from one-half to 2.25? Express your answer as a common fraction.

Answer: 2.25-0.5 = 1.75 = 7/4; 2/3*7/4 = 7/6

Jan 24: The length of a rectangular sports field is three times its width. If the perimeter of the field is 880 meters, what is the area of the field?

Answer: 110*330 = 363000

Jan 25: Josh mowed one-third of a 2000 square foot lawn in 18 minutes. At the same rate, how many minutes would it take him to mow a 4200 square foot lawn? Express your answer to the nearest whole number.

Answer: number of square foot per minute = (2000/3 )/ 18 = 1000/27 sq-ft/min; 4200 / (1000/27) = 27*42/10 = 113.4min. Nearest whole number is 114.

Jan 26: A bag contains 20 purple and 40 green marbles. How many purple marbles need to be added so that 5/12 of the marbles will be green?

Answer: 40/(60+x) = 5/12 x= 36 purple marbles

Jan 27: Jesse added all but one of the first ten positive integers together. The sum was a perfect square. Which one of the first ten positive integers did Jesse not include?

Answer: 6 (sum of first 10 positive integers is 55. 55-6 = 49.)

~~Click GoogleForm to submit answers by Sat, Jan 20.~~

Week of Jan 14– Jan 20

Jan 14: If a # b = a + 2b, for integers a and b, what is the value of 3 # 4?

Answer: 11

Jan 15: Kim chewed a piece of gum 42 times in one minute. If she continued to chew

at the same rate, how many times would she chew her gum in 100 seconds?

Answer: (42/60)*100 = 70

Jan 16: What is the average of the first 99 counting numbers?

Answer: 50

Jan 17: How many fewer minutes does it take to drive 35 miles at 30 mi/h than to drive the same distance at 25 mi/h?

Answer: 60 * (35 / 25 – 35 / 30) = 14

Jan 18: After a 20% reduction, the price of a computer was $800. What was the price of the computer before the reduction?

Answer: 1000

Jan 19: On a number line, what is the nearest integer to 4π?

Answer: 13

Jan 20: A shirt company charges a one-time setup fee plus a certain price per shirt. An order of 10 shirts costs $84. An order of 20 shirts costs $159. How much does an order of

30 shirts cost?

Answer: 10 shirts without setup fee is $159-$84 = $75. So 30 shirts with setup fee is $159+$75 = $ 234

~~Click GoogleForm to submit answers by Sat, Jan 13.~~

Week of Jan 7– Jan 13

Jan 7: If the digits 7, 8, 2, 3 and 0 are used, each exactly once, to form a three-digit positive integer and a two-digit positive integer that differ by exactly 288, what is the sum of the three-digit integer and the two-digit integer?

Answer: 452=370+82

Jan 8: How many diagonals are in a convex heptagon?

Answer: 7*4/2=14

Jan 9: What is the first year after 2018 that is a palindrome?

Answer: 2112

Jan 10: A standard 52-card deck of playing cards includes four aces. What is the probability that two cards selected randomly, without replacement, will both be aces? Express your answer as a common fraction.

Answer: (4/52)*(3/51) = 1/221

Jan 11: What is the value of ? Express your answer in simplest radical form.

Answer:

Jan 12:The temperature dropped from 13 °F to −5 °F. How many degrees Fahrenheit is the absolute value of the change in temperature?

Answer: 18

Jan 13: In rectangle ABCD, point P lies on side BC and point Q lies in the interior of the rectangle so that triangle APQ is equilateral. If the measure of angle PAB is 17 degrees, what is the measure of angle QPC?

Answer: 47 deg. Angle BPA = 73 deg; angle APQ = 60 deg. So angle QPC = 180 – angle BPA – angle APQ = 47.

Happy 2018! We are going to work on problems related to the number 2018.

~~Click GoogleForm to submit answers by Sat, Jan 6.~~

Week of Dec 31 – Jan 6

Dec 31: Jan 1, 2018 is the first day of the New Year. The 2018th day starting Jan 1, 2018 is __/__/____.

Answer: 7/11/2023 (2018 -2022 have 365*5+1 = 1826 days — 2020 is a leap year. 2018-1826 = 192 days in 2023. Jan-June have 181 days.)

Jan 1: Jan 1, 2018, the first day of the New Year, is a Monday. What day of the week is the 2018th day?

Answer: Tue (2017 mod 7 = 1)

Jan 2: New Year starts 00:00am on Jan 1. The 2018th minute is __:__ (am or pm)

Answer: 9:38am (2018-60*24=578; 578/60 = 9 R 38)

Jan 3: What is the largest prime factor of 2018?

Answer: 1009

Jan 4: What is the largest square number smaller than 2018?

Answer: 44*44=1936

Jan 5: What is the smallest power of 2 greater than 2018? (Examples of powers of 2: 1, 2, 4, 8, 16, 32, 64 …)

Answer: 2048

Jan 6: What is the sum of multiples of 18 that are smaller than 2018?

Answer: 113904 = (18+2016)/2*(2016/18)