Form the biggest squaring number
Clash Royale CLAN TAG#URR8PPP
up vote
9
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You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:
- Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)
- Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)
- You may apply this as many times as you want. ($(13)$ -> $169$ then $(16)9$->$2569$)
What is the biggest final number you can have?
mathematics formation-of-numbers
edited Sep 17 at 9:24
xhienne
3,337529
asked Sep 16 at 16:17
Oray
15.1k435145
 |Â
show 2 more comments
up vote
9
down vote
favorite
You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:
- Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)
- Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)
- You may apply this as many times as you want. ($(13)$ -> $169$ then $(16)9$->$2569$)
What is the biggest final number you can have?
mathematics formation-of-numbers
edited Sep 17 at 9:24
xhienne
3,337529
asked Sep 16 at 16:17
Oray
15.1k435145
1
Biggest final number? or biggest starting number?
– SteveV
Sep 16 at 16:33
is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
Sep 16 at 17:11
@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
Sep 16 at 17:12
$1(69) -> 14761$. Isn't this a violation of the previous rule?
– Wais Kamal
Sep 16 at 17:52
@WaisKamal ops true :) fixed it.
– Oray
Sep 16 at 17:53
 |Â
show 2 more comments
up vote
9
down vote
favorite
up vote
9
down vote
favorite
You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:
- Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)
- Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)
- You may apply this as many times as you want. ($(13)$ -> $169$ then $(16)9$->$2569$)
What is the biggest final number you can have?
mathematics formation-of-numbers
edited Sep 17 at 9:24
xhienne
3,337529
asked Sep 16 at 16:17
Oray
15.1k435145
You are going to start from any number with distinct digits lower than four digits (such as $a$, $ab$, $abc$) and you will apply the rule below:
- Take the square any number you want in the number (you may take the square the number itself too). (such as $1(02)$ -> $14$, or $12(3)$ -> $129$ or $(13)$ -> $169$)
- Every number you found has to have distinct digits. (Fail example: $(12)3$-> $1443$ X)
- You may apply this as many times as you want. ($(13)$ -> $169$ then $(16)9$->$2569$)
What is the biggest final number you can have?
mathematics formation-of-numbers
mathematics formation-of-numbers
edited Sep 17 at 9:24
xhienne
3,337529
asked Sep 16 at 16:17
Oray
15.1k435145
edited Sep 17 at 9:24
xhienne
3,337529
asked Sep 16 at 16:17
Oray
15.1k435145
edited Sep 17 at 9:24
xhienne
3,337529
edited Sep 17 at 9:24
xhienne
3,337529
edited Sep 17 at 9:24
xhienne
3,337529
3,337529
asked Sep 16 at 16:17
Oray
15.1k435145
asked Sep 16 at 16:17
Oray
15.1k435145
asked Sep 16 at 16:17
Oray
15.1k435145
15.1k435145
1
Biggest final number? or biggest starting number?
– SteveV
Sep 16 at 16:33
is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
Sep 16 at 17:11
@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
Sep 16 at 17:12
$1(69) -> 14761$. Isn't this a violation of the previous rule?
– Wais Kamal
Sep 16 at 17:52
@WaisKamal ops true :) fixed it.
– Oray
Sep 16 at 17:53
 |Â
show 2 more comments
1
Biggest final number? or biggest starting number?
– SteveV
Sep 16 at 16:33
is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
Sep 16 at 17:11
@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
Sep 16 at 17:12
$1(69) -> 14761$. Isn't this a violation of the previous rule?
– Wais Kamal
Sep 16 at 17:52
@WaisKamal ops true :) fixed it.
– Oray
Sep 16 at 17:53
1
1
Biggest final number? or biggest starting number?
– SteveV
Sep 16 at 16:33
Biggest final number? or biggest starting number?
– SteveV
Sep 16 at 16:33
is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
Sep 16 at 17:11
is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
Sep 16 at 17:11
@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
Sep 16 at 17:12
@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
Sep 16 at 17:12
$1(69) -> 14761$. Isn't this a violation of the previous rule?
– Wais Kamal
Sep 16 at 17:52
$1(69) -> 14761$. Isn't this a violation of the previous rule?
– Wais Kamal
Sep 16 at 17:52
@WaisKamal ops true :) fixed it.
– Oray
Sep 16 at 17:53
@WaisKamal ops true :) fixed it.
– Oray
Sep 16 at 17:53
 |Â
show 2 more comments
1 Answer
1
active
oldest
votes
up vote
8
down vote
accepted
Update:
I've found
9857240136 to be maximal (confirmed with programming).
Many possible ways to reach it, here is one starting with...
(4)2 -> 16(2) -> 1(6)4 -> 1(3)64 -> (1964) -> 3857(2)96 -> 3857(496) -> (3)85724016 -> 98572401(6) -> 9857240136
Previous attempt:
My new record is:
9810362574
which can be reached via
(5)74 -> (25)74 -> (625)74 -> 3(9)062574 -> (3)81062574 -> 9810(6)2574 -> 9810362574
First attempt:
Not proven to be maximal at all, but I managed to reach
10 digits with 4817093625
The steps are:
(705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625
answered Sep 16 at 16:56
elias
7,84232151
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
8
down vote
accepted
Update:
I've found
9857240136 to be maximal (confirmed with programming).
Many possible ways to reach it, here is one starting with...
(4)2 -> 16(2) -> 1(6)4 -> 1(3)64 -> (1964) -> 3857(2)96 -> 3857(496) -> (3)85724016 -> 98572401(6) -> 9857240136
Previous attempt:
My new record is:
9810362574
which can be reached via
(5)74 -> (25)74 -> (625)74 -> 3(9)062574 -> (3)81062574 -> 9810(6)2574 -> 9810362574
First attempt:
Not proven to be maximal at all, but I managed to reach
10 digits with 4817093625
The steps are:
(705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625
answered Sep 16 at 16:56
elias
7,84232151
add a comment |Â
up vote
8
down vote
accepted
Update:
I've found
9857240136 to be maximal (confirmed with programming).
Many possible ways to reach it, here is one starting with...
(4)2 -> 16(2) -> 1(6)4 -> 1(3)64 -> (1964) -> 3857(2)96 -> 3857(496) -> (3)85724016 -> 98572401(6) -> 9857240136
Previous attempt:
My new record is:
9810362574
which can be reached via
(5)74 -> (25)74 -> (625)74 -> 3(9)062574 -> (3)81062574 -> 9810(6)2574 -> 9810362574
First attempt:
Not proven to be maximal at all, but I managed to reach
10 digits with 4817093625
The steps are:
(705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625
answered Sep 16 at 16:56
elias
7,84232151
add a comment |Â
up vote
8
down vote
accepted
up vote
8
down vote
accepted
Update:
I've found
9857240136 to be maximal (confirmed with programming).
Many possible ways to reach it, here is one starting with...
(4)2 -> 16(2) -> 1(6)4 -> 1(3)64 -> (1964) -> 3857(2)96 -> 3857(496) -> (3)85724016 -> 98572401(6) -> 9857240136
Previous attempt:
My new record is:
9810362574
which can be reached via
(5)74 -> (25)74 -> (625)74 -> 3(9)062574 -> (3)81062574 -> 9810(6)2574 -> 9810362574
First attempt:
Not proven to be maximal at all, but I managed to reach
10 digits with 4817093625
The steps are:
(705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625
answered Sep 16 at 16:56
elias
7,84232151
Update:
I've found
9857240136 to be maximal (confirmed with programming).
Many possible ways to reach it, here is one starting with...
(4)2 -> 16(2) -> 1(6)4 -> 1(3)64 -> (1964) -> 3857(2)96 -> 3857(496) -> (3)85724016 -> 98572401(6) -> 9857240136
Previous attempt:
My new record is:
9810362574
which can be reached via
(5)74 -> (25)74 -> (625)74 -> 3(9)062574 -> (3)81062574 -> 9810(6)2574 -> 9810362574
First attempt:
Not proven to be maximal at all, but I managed to reach
10 digits with 4817093625
The steps are:
(705) -> 4(9)7025 -> 48170(25) -> 48170(6)25 -> 48170(3)625 -> 481709(6)25 -> 4817093625
answered Sep 16 at 16:56
elias
7,84232151
edited Sep 16 at 19:06
answered Sep 16 at 16:56
elias
7,84232151
answered Sep 16 at 16:56
elias
7,84232151
answered Sep 16 at 16:56
elias
7,84232151
7,84232151
add a comment |Â
add a comment |Â
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1
Biggest final number? or biggest starting number?
– SteveV
Sep 16 at 16:33
is there a restriction about how many digits the number which we square can have? like, if I get a number like 1023 as an interim result (even though 1023 itself is not possible), am I allowed to square it all to get to 1046529?
– elias
Sep 16 at 17:11
@elias "you may take the square the number itself too". written on the first rule. no restriction.
– Oray
Sep 16 at 17:12
$1(69) -> 14761$. Isn't this a violation of the previous rule?
– Wais Kamal
Sep 16 at 17:52
@WaisKamal ops true :) fixed it.
– Oray
Sep 16 at 17:53