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3 Digit Number - Maths Investigations
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Introduction
CWK1
3 Digit Number
Take any 3 digit number, write down all possible numbers that can be made with the three digits, add them up, divide the total by the sum of the 3 digits. Investigate.
If All Digits Are Different : -
123 456 789
132 465 798
213 546 879
231 564 897
321 654 987
+312 +645 +978
1332÷ 24=2223330 ÷ 15=2225328 ÷ 24=222
147 258 369
174 285 396
471 528 639
417 582 693
741 825 936
+714 _ +852 +963
2664÷ 12=2223330 ÷ 15=2223996 ÷ 18=222
It seems that when all 3 digits are different the answer to the problem is 222.
Can I use Algebra to explain this?
abc=100a+10b+c
acb=100a+10c+b
bac=100b+10a+c
bca=100b+10c+a
cba=100c+10b+a
+cab=100c+10a+b
222a+222b+222c = 222(a+b+c)
a+b+c
=222
What if 2 of the 3 digits are the same?
If 2 digits are the same : -
223 334 566
322 343 656
+232 +433 +665
777÷ 7=1111110 ÷ 10=1111887 ÷ 17=111
224 559 772
242 595 727
+422 +955 +277
888÷ 8=1112109 ÷19=111 1776 ÷ 16=111
Middle
=111
What if all 3 digits are the same number?
If All Digits Are The Same : -
333 = 37444 = 37666 = 37999 = 37777 _ = 37
9 12 18 27 21
It seems that when all the 3 digits are the same number the answer to the problem is 37.
Can I use Algebra to explain this?
aaa=100a+10a+a
=111a = 37
3a
What if
Conclusion
+cbaa=1000c+100b+10a+a
6666a+3333b+3333c
2a+b+c
=3333(2a+b+c) =3333
2a+b+c
What if 3 of the 4 digits are the same?
If 3 Of The 4 Digits Are The Same : -
4447
4474
4744
+7444
21109÷19=1111
Is this the same answer every time 3 of the 4 digits are the same?
Lets usr Algebraic terms to find out.
aaab=1000a+100a+10a+b
aaba=1000a+100a+10b+a
abaa=1000a+100b+10a+a
baaa=1000b+100a+10a+a
3333a+1111b
3a+b
=1111(3a+b) =1111
3a+b
What if all 4 digits are the same?
If All 4 Digits Are The Same : -
9999 =277.75
36
Is this the same answer every time all 4 digits are the same?
Let’s use Algebraic terms to find out.
aaaa=1000a+100a+10a+a
=1111a =277.75
4a
What if I do the same problem but with 5 digits instead of 4 or 3?
From the data I have gathered maybe I can guess the outcomes for 5 digits.
5 Digit Number
If All 5 Digits Are Different : -
This student written piece of work is one of many that can be found in our GCSE Pythagorean Triples section.
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