8

Part of 2016 AIME Problems

Problems(2)

Permutation of digits

Source: 2016 AIME I #8

For a permutation

p = (a_1,a_2,\ldots,a_9)

1,2,\ldots,9

s(p)

denote the sum of the three

3

a_1a_2a_3

a_4a_5a_6

a_7a_8a_9

m

be the minimum value of

s(p)

subject to the condition that the units digit of

s(p)

0

n

denote the number of permutations

p

s(p) = m

|m - n|

AMCAIMEAIME I2016 AIME Ipermutations

A PRODUCTive problem

Source: 2016 AIME II #8

Find the number of sets

\{a,b,c\}

of three distinct positive integers with the property that the product of

a,b,

c

is equal to the product of

11,21,31,41,51,

61