Primes and Squares

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7
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Place a different prime or square number on each of the fifteen disks below so that the number in any disk that lies on two others is the sum of the numbers in those disks. Do so in such a way that the number on the apex is as small as possible.

enter image description here

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

is this something you composed yourself?
– Kate Gregory
Nov 26 at 15:13

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
Nov 26 at 15:15

Zero (as a square) allowed?
– z100
Nov 26 at 20:43

1

@z100 You could not use a zero, since $x + 0 = x$, and therefore you'd have to have two $x$'es in your grid; that is disallowed. See imgur.com/a/gPWWkaN for explanation.
– Hugh
Nov 26 at 21:55

add a comment |

up vote
7
down vote

favorite

enter image description here

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

is this something you composed yourself?
– Kate Gregory
Nov 26 at 15:13

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
Nov 26 at 15:15

Zero (as a square) allowed?
– z100
Nov 26 at 20:43

1

@z100 You could not use a zero, since $x + 0 = x$, and therefore you'd have to have two $x$'es in your grid; that is disallowed. See imgur.com/a/gPWWkaN for explanation.
– Hugh
Nov 26 at 21:55

add a comment |

up vote
7
down vote

favorite

enter image description here

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

enter image description here

mathematics arithmetic

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

asked Nov 26 at 14:59

Bernardo Recamán Santos

2,2931141

is this something you composed yourself?
– Kate Gregory
Nov 26 at 15:13

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
Nov 26 at 15:15

Zero (as a square) allowed?
– z100
Nov 26 at 20:43

1

@z100 You could not use a zero, since $x + 0 = x$, and therefore you'd have to have two $x$'es in your grid; that is disallowed. See imgur.com/a/gPWWkaN for explanation.
– Hugh
Nov 26 at 21:55

add a comment |

is this something you composed yourself?
– Kate Gregory
Nov 26 at 15:13

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
Nov 26 at 15:15

Zero (as a square) allowed?
– z100
Nov 26 at 20:43

1

@z100 You could not use a zero, since $x + 0 = x$, and therefore you'd have to have two $x$'es in your grid; that is disallowed. See imgur.com/a/gPWWkaN for explanation.
– Hugh
Nov 26 at 21:55

is this something you composed yourself?
– Kate Gregory
Nov 26 at 15:13

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
Nov 26 at 15:15

Zero (as a square) allowed?
– z100
Nov 26 at 20:43

@z100 You could not use a zero, since $x + 0 = x$, and therefore you'd have to have two $x$'es in your grid; that is disallowed. See imgur.com/a/gPWWkaN for explanation.
– Hugh
Nov 26 at 21:55

add a comment |

2 Answers
2

active

oldest

votes

up vote
8
down vote

accepted

A much lower upper bound, which I'm fairly sure is optimal (assuming 0 is disallowed).

              1669 
           576 || 1093 
       383 || 193 || 900 
    347 ||  36 || 157 || 743 
 324 || 23 ||  13 || 144 || 599

edited Nov 26 at 21:20

answered Nov 26 at 20:28

B. Mehta

1963

Algorithm used extening the order? E.G.: 1st order: 1 ; 2nd order: 3 (1 2) ; 3rd order: 16 (3 13) (1 2 11) ; or 16 (13 3) (12 1 2) ;
– z100
Nov 26 at 21:25

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
Nov 26 at 21:33

1

My own (extremely shameful, dirty, brute-force) code confirms this answer is optimal. I can also provide the smallest apex value for a 4-level tree, which is 23.
– benj2240
Nov 27 at 1:03

1

@BernardoRecamánSantos Oh! You're right, 23 isn't possible. I didn't notice that I had a duplicated 3... Dirty code leads to dirty bugs. Let me correct myself: The smallest apex value for a 4-level tree is 59.
– benj2240
Nov 28 at 1:14

1

@benj2240: Yes, 59 is the lowest my students have achieved.
– Bernardo Recamán Santos
Nov 28 at 1:18

|
show 1 more comment

up vote
5
down vote

Alright, I’ve definitely got an upper bound here.

In text:

                  390625 
             140625 || 250000 
         50625 || 90000 || 160000 
     18225 || 32400 || 57600 || 102400 
 6561 || 11664 || 20736 || 36864 || 65536

However,

this uses all square numbers, and is far from optimal. I’ll have to see if I can reduce it by using primes.

edited Nov 26 at 16:51

gabbo1092

4,683738

answered Nov 26 at 16:32

Excited Raichu

4,777754

add a comment |

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
8
down vote

accepted

A much lower upper bound, which I'm fairly sure is optimal (assuming 0 is disallowed).

              1669 
           576 || 1093 
       383 || 193 || 900 
    347 ||  36 || 157 || 743 
 324 || 23 ||  13 || 144 || 599

edited Nov 26 at 21:20

answered Nov 26 at 20:28

B. Mehta

1963

Algorithm used extening the order? E.G.: 1st order: 1 ; 2nd order: 3 (1 2) ; 3rd order: 16 (3 13) (1 2 11) ; or 16 (13 3) (12 1 2) ;
– z100
Nov 26 at 21:25

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
Nov 26 at 21:33

1

My own (extremely shameful, dirty, brute-force) code confirms this answer is optimal. I can also provide the smallest apex value for a 4-level tree, which is 23.
– benj2240
Nov 27 at 1:03

1

@BernardoRecamánSantos Oh! You're right, 23 isn't possible. I didn't notice that I had a duplicated 3... Dirty code leads to dirty bugs. Let me correct myself: The smallest apex value for a 4-level tree is 59.
– benj2240
Nov 28 at 1:14

1

@benj2240: Yes, 59 is the lowest my students have achieved.
– Bernardo Recamán Santos
Nov 28 at 1:18

|
show 1 more comment

up vote
8
down vote

accepted

A much lower upper bound, which I'm fairly sure is optimal (assuming 0 is disallowed).

              1669 
           576 || 1093 
       383 || 193 || 900 
    347 ||  36 || 157 || 743 
 324 || 23 ||  13 || 144 || 599

edited Nov 26 at 21:20

answered Nov 26 at 20:28

B. Mehta

1963

Algorithm used extening the order? E.G.: 1st order: 1 ; 2nd order: 3 (1 2) ; 3rd order: 16 (3 13) (1 2 11) ; or 16 (13 3) (12 1 2) ;
– z100
Nov 26 at 21:25

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
Nov 26 at 21:33

1

My own (extremely shameful, dirty, brute-force) code confirms this answer is optimal. I can also provide the smallest apex value for a 4-level tree, which is 23.
– benj2240
Nov 27 at 1:03

1

@BernardoRecamánSantos Oh! You're right, 23 isn't possible. I didn't notice that I had a duplicated 3... Dirty code leads to dirty bugs. Let me correct myself: The smallest apex value for a 4-level tree is 59.
– benj2240
Nov 28 at 1:14

1

@benj2240: Yes, 59 is the lowest my students have achieved.
– Bernardo Recamán Santos
Nov 28 at 1:18

|
show 1 more comment

up vote
8
down vote

accepted

A much lower upper bound, which I'm fairly sure is optimal (assuming 0 is disallowed).

              1669 
           576 || 1093 
       383 || 193 || 900 
    347 ||  36 || 157 || 743 
 324 || 23 ||  13 || 144 || 599

edited Nov 26 at 21:20

answered Nov 26 at 20:28

B. Mehta

1963

A much lower upper bound, which I'm fairly sure is optimal (assuming 0 is disallowed).

              1669 
           576 || 1093 
       383 || 193 || 900 
    347 ||  36 || 157 || 743 
 324 || 23 ||  13 || 144 || 599

edited Nov 26 at 21:20

answered Nov 26 at 20:28

B. Mehta

1963

edited Nov 26 at 21:20

answered Nov 26 at 20:28

B. Mehta

1963

answered Nov 26 at 20:28

B. Mehta

1963

answered Nov 26 at 20:28

B. Mehta

1963

Algorithm used extening the order? E.G.: 1st order: 1 ; 2nd order: 3 (1 2) ; 3rd order: 16 (3 13) (1 2 11) ; or 16 (13 3) (12 1 2) ;
– z100
Nov 26 at 21:25

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
Nov 26 at 21:33

1

My own (extremely shameful, dirty, brute-force) code confirms this answer is optimal. I can also provide the smallest apex value for a 4-level tree, which is 23.
– benj2240
Nov 27 at 1:03

1

@BernardoRecamánSantos Oh! You're right, 23 isn't possible. I didn't notice that I had a duplicated 3... Dirty code leads to dirty bugs. Let me correct myself: The smallest apex value for a 4-level tree is 59.
– benj2240
Nov 28 at 1:14

1

@benj2240: Yes, 59 is the lowest my students have achieved.
– Bernardo Recamán Santos
Nov 28 at 1:18

|
show 1 more comment

Algorithm used extening the order? E.G.: 1st order: 1 ; 2nd order: 3 (1 2) ; 3rd order: 16 (3 13) (1 2 11) ; or 16 (13 3) (12 1 2) ;
– z100
Nov 26 at 21:25

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
Nov 26 at 21:33

1

My own (extremely shameful, dirty, brute-force) code confirms this answer is optimal. I can also provide the smallest apex value for a 4-level tree, which is 23.
– benj2240
Nov 27 at 1:03

1

@BernardoRecamánSantos Oh! You're right, 23 isn't possible. I didn't notice that I had a duplicated 3... Dirty code leads to dirty bugs. Let me correct myself: The smallest apex value for a 4-level tree is 59.
– benj2240
Nov 28 at 1:14

1

@benj2240: Yes, 59 is the lowest my students have achieved.
– Bernardo Recamán Santos
Nov 28 at 1:18

Algorithm used extening the order? E.G.: 1st order: 1 ; 2nd order: 3 (1 2) ; 3rd order: 16 (3 13) (1 2 11) ; or 16 (13 3) (12 1 2) ;
– z100
Nov 26 at 21:25

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
Nov 26 at 21:33

My own (extremely shameful, dirty, brute-force) code confirms this answer is optimal. I can also provide the smallest apex value for a 4-level tree, which is 23.
– benj2240
Nov 27 at 1:03

@BernardoRecamánSantos Oh! You're right, 23 isn't possible. I didn't notice that I had a duplicated 3... Dirty code leads to dirty bugs. Let me correct myself: The smallest apex value for a 4-level tree is 59.
– benj2240
Nov 28 at 1:14

@benj2240: Yes, 59 is the lowest my students have achieved.
– Bernardo Recamán Santos
Nov 28 at 1:18

|
show 1 more comment

up vote
5
down vote

Alright, I’ve definitely got an upper bound here.

In text:

                  390625 
             140625 || 250000 
         50625 || 90000 || 160000 
     18225 || 32400 || 57600 || 102400 
 6561 || 11664 || 20736 || 36864 || 65536

However,

this uses all square numbers, and is far from optimal. I’ll have to see if I can reduce it by using primes.

edited Nov 26 at 16:51

gabbo1092

4,683738

answered Nov 26 at 16:32

Excited Raichu

4,777754

add a comment |

up vote
5
down vote

Alright, I’ve definitely got an upper bound here.

In text:

                  390625 
             140625 || 250000 
         50625 || 90000 || 160000 
     18225 || 32400 || 57600 || 102400 
 6561 || 11664 || 20736 || 36864 || 65536

However,

this uses all square numbers, and is far from optimal. I’ll have to see if I can reduce it by using primes.

edited Nov 26 at 16:51

gabbo1092

4,683738

answered Nov 26 at 16:32

Excited Raichu

4,777754

add a comment |

up vote
5
down vote

Alright, I’ve definitely got an upper bound here.

In text:

                  390625 
             140625 || 250000 
         50625 || 90000 || 160000 
     18225 || 32400 || 57600 || 102400 
 6561 || 11664 || 20736 || 36864 || 65536

However,

this uses all square numbers, and is far from optimal. I’ll have to see if I can reduce it by using primes.

edited Nov 26 at 16:51

gabbo1092

4,683738

answered Nov 26 at 16:32

Excited Raichu

4,777754

Alright, I’ve definitely got an upper bound here.

In text:

                  390625 
             140625 || 250000 
         50625 || 90000 || 160000 
     18225 || 32400 || 57600 || 102400 
 6561 || 11664 || 20736 || 36864 || 65536

However,

this uses all square numbers, and is far from optimal. I’ll have to see if I can reduce it by using primes.

edited Nov 26 at 16:51

gabbo1092

4,683738

answered Nov 26 at 16:32

Excited Raichu

4,777754

edited Nov 26 at 16:51

gabbo1092

4,683738

edited Nov 26 at 16:51

gabbo1092

4,683738

edited Nov 26 at 16:51

gabbo1092

4,683738

answered Nov 26 at 16:32

Excited Raichu

4,777754

answered Nov 26 at 16:32

Excited Raichu

4,777754

answered Nov 26 at 16:32

Excited Raichu

4,777754

add a comment |

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