Prealgebra question

Question

Rustam likes multiples of 5. For his RSM project he makes up numbers such that any two of the digits of any of his numbers, when put next to each other in some order, make a two-digit multiple of 5. His teacher calls such numbers Rustam’s numbers. For example, the numbers 51 and 502 are Rustam’s numbers, but the numbers 300 and 2018 are not. How many different three-digit Rustam’s numbers with none of the digits greater than 5 are there?

Answer 1

Why is 300 not a Rustam number?

30/5 = 6

Why is 2018 not a Rustam number?

20/5 = 4

The definition says "ANY TWO DIGITS IN ANY ORDER THAT

FORM A MULTIPLE OF 5"

So basically, the number CANNOT have zeros, nor five 5.

Otherwise it shall qualify as a Rustam number per the definition.

So ZEROS AND FIVES ARE NOT ALLOWED

111,112,113,114,116,117,118,119

121,122,123,124,126,127,128,129

131,132,133,134,136,137,138,139

141,142,143,144,146,147,148,149

see the pattern????

191,192,193,194,196,197,198,199

211,212,213,214,216,217,218,219

221,222,223,224,226,227,228,229

the pattern continues....

291,292,293,294,296,297,298,299

same thing holds for groups of 300s, 400s, 500s,

600s, 700s, 800, 900s

8 numbers in each row.

9 rows

9 groups

8 * 9 * 9 = 8 * 81 = 648 of the 3-digit Rustam numbers