Uncreative Title For a Math(s) Problem

Number Theory Level 2

Æ of a said number equal the sum of all digits in said number. if the the sum is a 2 or more digit number you repeat until you get to a 1 digit number. for example:

Æ ( 289 ) = 2 + 8 + 9 = 19 = 1 + 9 = 10 = 1 + 0 = 1 Æ(289) = 2+8+9 = 19 = 1+9 = 10 = 1+0 = 1

so the answer to Æ of 289 is 1. Without doing all the math what is equal:

Æ ( 13 ∗ 71 ∗ 84 ∗ 28 ∗ 102 ) Æ(13*71*84*28*102)

9 5 7 2 1 8

Diego Zequeira-Russell by Diego Zequeira-Russell , 16, USA

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2 solutions

Cantdo Math
Apr 21, 2020

SInce,the number is divisible by 9 at the beggining.It will be so at the end.Hence,the answer is 9.(since the sum of digit of a number =the number modulo 9)

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This function is more commonly known as the digital root of a number. For most numbers there is a pattern when using this function. like if you look at the multiples of 7.

7 = 7 14 = 5 21 = 3 28 = 1 35 = 8 42 = 6.....

you can see that these numbers are going down by 2 each time. 7 5 3 1. After getting to 0 the cycle back to 9. It goes down/up different amounts for each number. 3 = 3 or -6 4 = 4 -5 5 = 5 or -4 6 = 6 or -3 7 = 7 or -2 8 = 8 or -1 9 = 9 since 9 is 9 it just does all the way around and back to 9 every time. So a multiply of 9 will always be 9. In the question the number is a multiple of 9 because there are 2 multiples of 3 (84 and 102). So the answer is 9 \fbox{9}

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