Subject: studdent from Australia, yr 12 (final year)

hello. i am kylie mcalpine and a final year student in Perth, western australia. i was told about this webstie so i decided to ask for your assistance in and investigation i am currently doing at school

there are 3 tables

n3n
13
29
327
481
5243
62187
76561
819683
859049

the other 2 tables included are n to the power of 7, n being 1-10 and the other is 4 to the power of n i have figured out the patterns for the tables, the last digits in the table of 3 forms a continuos pattern of 3,9,1,7

the other tables have patterns as well. table 7 has the pattern of 7,,9,3,1 and table 4 has the pattern of 4,6,4,6 etc.

the questions we have been asked are what is the units digit of the following:

a) 358
b) 2358
c) 1731

and the harder question of:

what is the units digit of the following sum: 13841 + 17508 + 24617 = ???????

if there is any information i have not included, please inform me.

thankyou again
kylie

Hi Kylie,

Here is an outline of how to do it:
In the 3 to the power of n table, the pattern can be developed without calculating each power:

power of 3calculationunit digit
31 3
323x3=99
339x3=277
347x3=211
351x3=33
etc  

The pattern repeats every four digits.

Imagine that you complete this table to 58 rows. 58/4 = 14 with a REMAINDER 2 so the pattern repeats 14 times and then there are two more rows with 3 and 9 in the units digit column. Thus the units digit of 358 is 9.

Using the same technique you can complete the next two problems.

For the harder question use the above technique to find the units digit of each of 13841, 17508 and 24617.

Cheers,
Paul and Penny
Go to Math Central