### The Level E problems can be solved by elementary school math. They are designed from CMM Level E students, though students in Level M may find them interesting too. The answer to each problem should be a number. Please also report how many minutes it takes you to finish each problem. Do not rush. Do not use a calculator.

14th Assignment (Due: 8:00pm ET, June 30, 2020)

E1. In the expression LOGO + SHOT = HARD, each letter represents a single digit number from 0 to 9. Different letters represent different numbers. L, S and H cannot be zero. What's the difference between the largest and smallest values of HARD?

E2. 30 CMM students get together and discuss their favorite math subjects. 23 of them like geometry; 29 of them like algebra; 19 of them like probability. At most how many students like all three subjects?

E3. Leo's mom asks Dr. Hong, Leo and Angela to clean up the house. If Dr. Hong and Leo work together, they can complete the task in 1.5 hours. If Dr. Hong and Angela work together, it would take them 1.75 hours. If Leo and Angela work together, it would take them 4.2 hours. If all three of them work together, how long does it take to clean up the house?

M1. Points A, B and C are the pairwise points of tangency of three externally tangent circles of radius 1. What's the area surrounded by the arcs AB, BC and CA?

M2. After Dr. Hong, Leo and William complete a basketball workout, they open a pack of Oreo cookies to share among themselves. If there are 12 cookies in the pack, and if each person gets at least one cookie, how many different ways are there to distribute the cookies? (They do not split a cookie.)

M3. Math Kangaroo is a popular math contest. There are 24 questions in the test. Each question has point value. 1/3 of questions are 3 points each; 1/3 are 4 points each, 1/3 are 5 points each. The sum of earned points is the student's final score. Leo and five other kids join the contest. The median and mean of their scores are both 90. If they all have different scores, what's the lowest possible score among them?

Previous Meetups

 Date Assignment Solution WK1 3/24; 3/26 A1 WK2 3/31; 4/2 A2 WK3(E) 4/7 A3E A3E WK3(M) 4/9 A3M A3M WK4(E) 4/14 A4E A4E WK4(M) 4/16 A4M A4M WK5(E) 4/21 A5E A5E WK5(M) 4/23 A5M A5M WK6(E) 4/28 A6E A6E WK6(M) 4/30 A6M A6M WK7(E) 5/5 A7E A7E WK7(M) 5/7 A7M A7M WK8 5/14 A8E; A8M A8 WK9 5/21 A9E; A9M A9 WK10 5/28 A10E; A10M A10 WK11 6/4 A11E; A11M A11 WK12 6/11 A12E; A12M A12 WK13 6/24 A13E; A13M A13 WK14 7/1 A14E; A14M A14