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Hints and solutions to
Problem of the day for Thursday, May 28
List these numbers from smallest to largest:
2121, 955, 788.
- We had one like this before, where the numbers were too big for our
calculators.
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But as before, we can notice that the exponents are all multiples of
11.
So we're really dealing with the numbers (211)11,
(95)11, and (78)11.
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That means we really have to put the numbers 211,
95,
and 78 in order. These are numbers we can do either by hand or
by calculator.
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And we get 211 = 2024, 95 = 59,049, and
78 = 5,764,801.
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Or, if you want to be independent and do the whole thing by hand, you
could notice that 95 > 85 =
(23)5 = 215 > 211,
so 211 is less than 95.
- Then you could notice that
78 > 68 = (28)(38)
= (28)(94) > 9(94) = 95.
Therefore 95 is less than 78.
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In any case, we conclude that the numbers were in order to begin with:
2121 < 955 < 788
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