On day one Conner collects 32 rocks because 8 x 4 = <<8*4=32>>32

On day three Sydney collects 64 because 32 x 2 = <<32*2=64>>64

After three days Sydney has 915 rocks because 837 + 0 + 4 + 64 =<<837+0+4+64=905>>905

Before the third day Conner has 878 because 723 + 32 + 123 = <<723+32+123=878>>878

Conner needs to collect 37 on day three to tie Sydney because 905 - 878 = 27

# Answer

27
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Sydney and Conner are having a three day rock collecting contest to see who can have the largest collection after adding to their existing collections. Before they start, Sydney has 837 rocks and Conner has 723. On day one, Sydney collects 4 rocks and Conner collects 8 times as many. On day two Sydney rests and Conner collects 123. On the third day, Sydney collects twice as many as Conner did on the first day. How many does Conner have to collect on day three to make sure he at least ties Sydney?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
27
Sydney and Conner are having a three day rock collecting contest to see who can have the largest collection after adding to their existing collections. Before they start, Sydney has 837 rocks and Conner has 723. On day one, Sydney collects 4 rocks and Conner collects 8 times as many. On day two Sydney rests and Conner collects 123. On the third day, Sydney collects twice as many as Conner did on the first day. How many does Conner have to collect on day three to make sure he at least ties Sydney?
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