The Critical Line – Volume 12

Read­ing time: 2 mins

Jevon Ful­brook brings us this month’s Crit­i­cal Line chal­lenge, with a puz­zling East­er-egg hunt!

Annie the actu­ary has sur­vived the Christ­mas par­ty and is now on East­er Break with her fam­i­ly.

She has set up an East­er egg hunt for her daugh­ter and her friends, but was over zeal­ous set­ting the clues!

The most dif­fi­cult one – and the clues to find the largest egg, were too hard for the chil­dren to solve and they have enlist­ed your help to solve them.

The loca­tion of the egg is reveal by fill­ing in the fol­low­ing by unscram­bling a set of let­ters;

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ !   _ _’_    _ _    _ _ _    _ _ _ _ _ _    _ _ _ _

To solve the loca­tion the chil­dren will need to unscram­ble cer­tain let­ters from the grid of let­ters giv­en below;

The let­ters to extract from the grid will be revealed by over­lay­ing the answer found by solv­ing the grid below.

Note that the fol­low­ing 4×4 grid should give you suf­fi­cient infor­ma­tion to work out how to solve the larg­er ver­sion. Good luck and move quick­ly, the East­er egg might be melt­ing or will be eat­en by some­thing else first!

For your chance to win $50, send your solu­tion to the puz­zle to ActuariesMag@actuaries.asn.au

The Critical Line – Volume 11 Solution

The most square num­bers found in a mag­ic square by read­ers was 7, which also match­es my own search.

Con­grat­u­la­tions to Corey Plover, Stephen Woods, Andrew Park­er and Adri­an Yiu who all sub­mit­ted the same solu­tion with a row sum of 541,875

3732

360721

2052

2892

4252

5272

5652

232

222121

The book vouch­er prize, drawn at ran­dom, goes to Stephen Woods.

Fur­ther inves­ti­gat­ing online has led me to con­clude that this is the ONLY 7-square 3×3 mag­ic square known to be pub­lished (not count­ing its reflec­tions, rota­tions and mul­ti­ples), and that no one has proven or dis­proven the pos­si­bil­i­ty of an 8-square or 9-square 3×3 mag­ic square.

I should also apol­o­gise for my sug­ges­tion in the orig­i­nal ques­tion that you can freely choose 4 num­bers and derive the oth­er 5 when con­struct­ing a 3×3 mag­ic square.  In fact you can freely choose only 3 val­ues, pro­vid­ed they are not all on the same one of the 4 lines pass­ing through the cen­tre, and the oth­er 6 are then derived.  And even then, there are some odd/even par­i­ty issues that can exclude cer­tain per­mu­ta­tions of 3 free num­bers.

For the record, here are the 3-square, 4-square, 5-square and 6-square cas­es with the small­est row sums.

4

9

2

 

16

19

4

 

55

49

16

 

25

289

121

3

5

7

 

1

13

25

 

1

40

79

 

241

145

49

8

1

6

 

22

7

10

 

64

31

25

 

169

1

265

 

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About the author

Jevon Fulbrook

Originally from Wellington, Jevon moved to Melbourne four years ago for study and fell in love with the city. He currently works as an actuarial analyst at coBERN. His spare time sees him involved in any combination of golf, woodworking and drinking beer.

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