(01/07/97) 

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MathMagic Cycle 23: Level 10-12 Regular 

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Patterns

1) Without the aid of algebra, try to find a two digit number that is
twice the sum of its digits.

2) A sequence of figures is built as follows:

                             x
                x           xxx
     x         xxx         xxxxx   etc...
    Fig.1      Fig.2       Fig.3

How many "x" are there in figure 100?

3) For this pattern:

                    1 + 2 = 3
                4 + 5 + 6 = 7 + 8
          9+ 10 + 11 + 12 = 13 + 14 + 15 ...

What is the last number in the 80th row going to be? 

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MathMagic Cycle 23: Level 10-12 Advanced 

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1) If the natural numbers are arranged in a triangular grid (see below),
what is the third number in the 50th row?

                          1
                       2  3  4
                    5  6  7  8  9 ...

2) What is the last digit of this exponent?

                          1992
                         3

3) What is the last digit of the product of these exponents?

                     1988      1988      1988
                    2      X  3      X  7

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Good luck
MrH