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# Divisibility/remainders

+2
57
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Jax bought exactly enough trees to plant eight equal rows. Then one tree died and couldn't be planted, but he still had enough trees left to plant exactly nine equal rows. After that, a tree was stolen, but he still had enough trees left to plant exactly ten equal rows. If he bought the least number of trees satisfying these three conditions, how many trees did he buy?

off-topic
Mar 3, 2020
edited by brianlaw  Mar 3, 2020

### 3+0 Answers

#1
+22043
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By brute force I find 352 trees

I started with multiples of 8 that were 2 more than a multiple of 10 .....then tried subtracting one to see if 9 would divide evenly.

Mar 3, 2020
#2
+109499
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Thanks, EP....!!!!

I contributed another "brute force"  answer, here :

https://web2.0calc.com/questions/help_60200

And   GA  contributes a  more  "mathematical" answer, here :

https://web2.0calc.com/questions/nice-question

I might  have  missed  some other answerers   [ sorry  !!!  ]

Mar 3, 2020
#3
+1

n mod 8 =0
n mod 9 =1
n mod 10 =2

The LCM of 8/2, 9, 10/2 =180

Using "Chinese Remainder Theorem + Modular Multiplicative Inverse"
180  +  172 = 352 minimum number of trees

Mar 3, 2020