MathDB

3

Part of 2010 Malaysia National Olympiad

Problems(3)

OMK 2010

Source: Malaysia National Olympiad 2010 Bongsu Category Problem 3

6/4/2011
Adam has RM2010 in his bank account. He donates RM10 to charity every day. His first donation is on Monday. On what day will he donate his last RM10?
combinatorics unsolvedcombinatorics
OMK 2010

Source: Malaysia National Olympiad 2010 Muda Category Problem 3

6/4/2011
Let γ=α×β\gamma=\alpha \times \beta where α=999⋯9\alpha=999 \cdots 9 (2010 '9') and β=444⋯4\beta=444 \cdots 4 (2010 '4') Find the sum of digits of γ\gamma.
number theory unsolvednumber theory
OMK 2010

Source: Malaysia National Olympiad 2010 Sulung Category Problem 3

6/4/2011
Let N=abc‾N=\overline{abc} be a three-digit number. It is known that we can construct an isoceles triangle with a,ba,b and cc as the length of sides. Determine how many possible three-digit number NN there are.
(N=abc‾N=\overline{abc} means that a,ba,b and cc are digits of NN, and not N=a×b×cN=a\times b\times c.)
combinatorics unsolvedcombinatorics