4. a) James has 15 sweets in his pocket. He has 7 rec! sweets, 6 blue sweets, one! 2 pink sweets. Without looking, be removes some sweets from his pocket one! places them on the table. What is the smallest number of sweets be should remove to guarantee that be has at least one sweet of each colour?
c) Karen wants to find the value of 1+2+3+4+5+6+7+8+9+10. Rather than just doing the calculation ,She notices that she can reorder the number is a clever way:
1+10+2+9+3+8+4+7+5+6 . She does this because 1+10, 2+9, 3+8 etc all add up to 11 , and so her sum simplifies to 11+11+11+11+11, which equals 55.
Using Karen's method , add up all of the whole numbers from 1 to 20.
d) Tina is an athlete , and she is completing a difficult training session. Her coach makes her run 5 metres forwards , then 5 metres back , then 10 metres forwards then 10 metres back , then 15 metres forwards, 15 metres back, and this continues until she has run 100 metres forwards, then 100 metres back.
How far does Tina run in total?