The numberabc has a decimal representation of ax10^{2} + bx10^{1} + cx10^{0}. But let's change things around a bit, and drop the base ten. We could then write abc = a^{2} + b^{1} + c^{0} and ask what values of a b c satisfy the equation. There actually may not be a solution. But if we play with the exponents a bit, we might come up with some numbers that do work. Try these

(The numbers are in order, smallest to largest.)

ab = a^{2} + b^{3}

cd = c^{2} + d^{3}

efg = e^{1} + f^{2} + g^{3}

hij = h^{1} + i^{2} + j^{3}

klm = k^{1} + l^{2} + m^{3}

nop = n^{1} + o^{2} + p^{3}

qrst = q^{1} + r^{2} + s^{3} + t^{4}

uvwx = u^{1} + v^{2} + w^{3} + x^{4}

yz@$ = y^{1} + z^{2} + @^{3} + $^{4}

There is a shorthand notation. These can also be written ab (2,3), cd (2,3), efg (1,3,5), ... yz@$ (1,2,3,4).

So here's a bonus challenge: abcdefgcc (4, 3, 8, 5, 7, 9, 0, 8, 8)

## Question

## bonanova 85

The number

has a decimal representation ofabcx10a^{2}+x10b^{1}+x10c^{0}. But let's change things around a bit, and drop the base ten. We could then write=abcand ask what values ofa^{2}+ b^{1}+ c^{0}satisfy the equation. There actually may not be a solution. But if we play with the exponents a bit, we might come up with some numbers that do work. Try thesea b c(The numbers are in order, smallest to largest.)

^{2}+ b^{3}^{2}+ d^{3}^{1}+ f^{2}+ g^{3}^{1}+ i^{2}+ j^{3}^{1}+ l^{2}+ m^{3}^{1}+ o^{2}+ p^{3}^{1}+ r^{2}+ s^{3}+ t^{4}^{1}+ v^{2}+ w^{3}+ x^{4}^{1}+ z^{2}+ @^{3}+ $^{4}There is a shorthand notation. These can also be written ab (2,3), cd (2,3), efg (1,3,5), ... yz@$ (1,2,3,4).

So here's a bonus challenge: abcdefgcc (4, 3, 8, 5, 7, 9, 0, 8, 8)

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