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?

sweets

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?

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