MathDB

5

Part of 2017 Hanoi Open Mathematics Competitions

Problems(2)

a, b, c are 2-digit, 3-digit, and 4-digit numbers (HOMC 2017 J Q5)

Source:

8/7/2019
Let a,b,ca, b, c be two-digit, three-digit, and four-digit numbers, respectively. Assume that the sum of all digits of number a+ba+b, and the sum of all digits of b+cb + c are all equal to 22. The largest value of a+b+ca + b + c is
(A): 10991099 (B): 20992099 (C): 11991199 (D): 21992199 (E): None of the above.
number theorymaximumDigits
replace x,y from 2017 numbers with x+7xy+y, last (HOMC 2017 S Q5)

Source:

9/9/2019
Write 20172017 following numbers on the blackboard: −10081008,−10071008,...,−11008,0,11008,21008,...,10071008,10081008-\frac{1008}{1008}, -\frac{1007}{1008}, ..., -\frac{1}{1008}, 0,\frac{1}{1008},\frac{2}{1008}, ... ,\frac{1007}{1008},\frac{1008}{1008} . One processes some steps as: erase two arbitrary numbers x,yx, y on the blackboard and then write on it the number x+7xy+yx + 7xy + y. After 20162016 steps, there is only one number. The last one on the blackboard is
(A): −11008-\frac{1}{1008} (B): 00 (C): 11008\frac{1}{1008} (D): −1441008-\frac{144}{1008} (E): None of the above
algebraFractioncombinatorics