OCR Further Discrete AS 2018 June — Question 2

Exam BoardOCR
ModuleFurther Discrete AS (Further Discrete AS)
Year2018
SessionJune
TopicCombinations & Selection

2 Mo eats exactly 6 doughnuts in 4 days.
  1. What does the pigeonhole principle tell you about the number of doughnuts Mo eats in a day? Mo eats exactly 6 doughnuts in 4 days, eating at least 1 doughnut each day.
  2. Show that there must be either two consecutive days or three consecutive days on which Mo eats a total of exactly 4 doughnuts. Mo eats exactly 3 identical jam doughnuts and exactly 3 identical iced doughnuts over the 4 days.
    The number of jam doughnuts eaten on the four days is recorded as a list, for example \(1,0,2,0\). The number of iced doughnuts eaten is not recorded.
  3. Show that 20 different such lists are possible.