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 16 hours ago

Bernardo Recamán Santos

2,1211138

is this something you composed yourself?
– Kate Gregory
15 hours ago

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
15 hours ago

Zero (as a square) allowed?
– z100
10 hours ago

@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
9 hours ago

add a comment |

up vote
7
down vote

favorite

enter image description here

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

is this something you composed yourself?
– Kate Gregory
15 hours ago

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
15 hours ago

Zero (as a square) allowed?
– z100
10 hours ago

@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
9 hours ago

add a comment |

up vote
7
down vote

favorite

enter image description here

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

enter image description here

mathematics arithmetic

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

asked 16 hours ago

Bernardo Recamán Santos

2,1211138

is this something you composed yourself?
– Kate Gregory
15 hours ago

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
15 hours ago

Zero (as a square) allowed?
– z100
10 hours ago

@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
9 hours ago

add a comment |

is this something you composed yourself?
– Kate Gregory
15 hours ago

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
15 hours ago

Zero (as a square) allowed?
– z100
10 hours ago

@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
9 hours ago

is this something you composed yourself?
– Kate Gregory
15 hours ago

@KateGregory: A variation on an old theme.
– Bernardo Recamán Santos
15 hours ago

Zero (as a square) allowed?
– z100
10 hours ago

@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
9 hours ago

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 9 hours ago

answered 10 hours ago

B. Mehta

1963

New contributor

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
9 hours ago

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
9 hours ago

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
6 hours ago

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 14 hours ago

gabbo1092

4,581735

answered 14 hours ago

Excited Raichu

4,283752

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 9 hours ago

answered 10 hours ago

B. Mehta

1963

New contributor

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
9 hours ago

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
9 hours ago

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
6 hours ago

add a 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 9 hours ago

answered 10 hours ago

B. Mehta

1963

New contributor

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
9 hours ago

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
9 hours ago

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
6 hours ago

add a 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 9 hours ago

answered 10 hours ago

B. Mehta

1963

New contributor

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 9 hours ago

answered 10 hours ago

B. Mehta

1963

New contributor

edited 9 hours ago

answered 10 hours ago

B. Mehta

1963

New contributor

answered 10 hours ago

B. Mehta

1963

answered 10 hours ago

B. Mehta

1963

New contributor

B. Mehta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

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
9 hours ago

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
9 hours ago

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
6 hours ago

add a 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
9 hours ago

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
9 hours ago

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
6 hours ago

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
9 hours ago

@z100 I'm afraid I'm not sure what you're asking - could you clarify?
– B. Mehta
9 hours ago

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
6 hours ago

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 14 hours ago

gabbo1092

4,581735

answered 14 hours ago

Excited Raichu

4,283752

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 14 hours ago

gabbo1092

4,581735

answered 14 hours ago

Excited Raichu

4,283752

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 14 hours ago

gabbo1092

4,581735

answered 14 hours ago

Excited Raichu

4,283752

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 14 hours ago

gabbo1092

4,581735

answered 14 hours ago

Excited Raichu

4,283752

edited 14 hours ago

gabbo1092

4,581735

edited 14 hours ago

gabbo1092

4,581735

edited 14 hours ago

gabbo1092

4,581735

answered 14 hours ago

Excited Raichu

4,283752

answered 14 hours ago

Excited Raichu

4,283752

answered 14 hours ago

Excited Raichu

4,283752

add a comment |

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