DISINI sol2013
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Point P is chosen in the interior of this triangle so that the area of triangles ABP , APC and PBC are all equal... If each element of S is converted to a decimal integer
We see that the units digit of 2 A + 2 (the two digits plus the carry) must equal 8.. Suppose that Anna guesses “cat” c times and guesses “dog” d times. 95 d are
(b) Prove that there is a sequence of replacements that will make the final number equal to 1000.. Lavaman versus
We now claim that there is a colouring of the board such that the number of blue- dominated columns plus the number of red-dominated rows is m + n − 2; Colour the first column
The total number of non-predictive sequences that begin PPQQ is equal to the number of ways of arranging the remaining 8 P’s and 1 Q in 9 positions. Since the Q can be placed in any
When the second coin is placed (in any one of 15 squares), 6 of the 15 squares will leave two coins in the same row or column and 9 of the 15 squares will leave the two coins
(Try blocking out the numbers larger than each of these to see this.) This pattern does continue since when each of these odd perfect squares is reached, the number of spaces up to
How many positive integers less than 100 are there such that the product of all positive divisors of such a number is equal to the square of the
