April 24, 2017

In the spring of 2013, Dahlia created a flower bed and planted one daffodil. The following spring, three daffodils bloomed. In fact, each spring, from 2013 to 2016, the number of daffodils that bloomed in Dahlia’s flower bed was 1, 3, 9 and 27, respectively. If this pattern continues, how many daffodils can Dahlia expect to bloom in the spring of 2017?

It appears that each year after 2013 the number of daffodils that bloomed in Dahlia’s garden was three times the number that bloomed the previous year. If this pattern continues, in 2017, Dahlia can expect there to be 27 × 3 = 81 blooms.

 

In the spring of 2013, Rose created a flower bed and planted two tulips. The following spring four tulips bloomed. Each spring, from 2013 to 2016, the number of tulips that bloomed in Rose’s flower bed was 2, 4, 8 and 16, respectively. If this pattern continues, what is the absolute difference in the number of tulips and daffodils expected to bloom in Rose’s and Dahlia’s flower beds in 2017?

It appears that every year since Rose planted two tulips in 2013, the number of tulips that bloomed was twice the number that bloomed the previous year. If this pattern continues, Rose can expect 16 ´ 2 = 32 tulips to bloom in 2017. The difference in the number tulips and daffodils that are expected to bloom in Rose’s and Dahlia’s gardens in 2017 is 81 – 32 = 49.

 

In the spring of 2013, Lily created a flower bed and planted three hyacinths. Each spring, from 2013 to 2016, the number of hyacinths that bloomed in Lily’s flower bed was 3, 6, 10 and 15, respectively. If this pattern continues, what is the total number of hyacinths that will have bloomed in Lily’s flower bed from the spring of 2013 through the spring of 2017?     

Lily planted 2 hyacinths in 2013. In 2014, the number of hyacinths that bloomed was three more than the number she planted in 2013. In 2015, the number of blooms in Lily’s garden was four more than the number of blooms in 2014, and in 2016 there were five more blooms than in 2015. If this pattern continues, Lily can expect the number of blooms in 2017 to be six more than in 2016, which would be 15 + 6 = 21 blooms. So, the total number of hyacinths in Lily’s garden from 2013 through 20174 was 3 + 6 + 10 + 15 + 21 = 55 hyacinths. (NOTE: Since the problem doesn’t explicitly indicate whether the flowers Lily planted in 2013 had already bloomed, one could also conclude that hyacinths bloomed in her garden only in 2014, 2015, 2016 and 2017. In which case, the total number of hyacinths that actually bloomed from 2013 to 2017 would be 6 + 10 + 15 + 21 = 52 hyacinths.)

 

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Page 2
contains ONLY PROBLEMS.