Base Five: What is one hand more than (3)_5? If you are not sure where you will

Question

Base Five:

What is one hand more than (3)_5? If you are not sure where you will land, actually count by ones until you have counted one hand more than three! a Record your result with a number word and digits. Count forwards by one hand again. Record this result with a number word and digits. Continue until you get to one arm four hand three, or (143)_5! b. What pattern do you notice in the digits you wrote down? Describe it. To do this, describe the pattern in the ones digit and the pattern in the hands digit. c How many hands do you count when you count by hands from (3)_5 to (103)_5? Please answer in base five. Explain your answer. d. Challenge: How many hands do you count when you count by hands from (3)_5 to (143)_5? Please answer in base five. Explain your answer.

Explanation / Answer

So BASE 5 Counting works in this way

0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24 ......

a) What is one hand more than (3)5 => 4,10,11, 12, 13
=> (13)5

b) (3)5 to (103)5 =>
4,
10, 11, 12, 13, 14,
20, 21, 22, 23, 24,
30, 31, 32, 33, 34,
40, 41, 42, 43, 44 ,
100,101, 102, 103

In this way it happens

Total rows = 5 , Take 3 as part of last row.
So we need total 5 hands when we count from (3)5 to (103)5


c) (3)5 to (143)5 =>
4,
10, 11, 12, 13, 14,
20, 21, 22, 23, 24,
30, 31, 32, 33, 34,
40, 41, 42, 43, 44 ,
100,101, 102, 103,104,
110,111, 112, 113, 114,
120,121, 122, 123, 124,
130,131, 132, 133, 134,
140,141, 142, 143
In this way it happens

Total rows = 9 , Take 3 as part of last row.
So we need total 9 hands when we count from (3)5 to (143)5

Thanks, let me know if you have any doubts

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