Answers<\/strong><\/p>\nPeople have reported 86 different sets of four numbers that add up to the magic constant of 34. The more obvious ones are\u2013 four rows, four columns, two diagonals, the four quadrants, the four numbers in the middle and the four numbers at each corner.<\/p>\n
The picture was made in year 1514 (clue: centre of bottom row)<\/p>\n<\/div><\/div><\/div>
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Square of the Cross<\/h4>\n<\/div>\n\n
Is it possible to arrange the digits 1 2 3 4 5 6 7 8 9, one in each square of the cross, such that the sum along the vertical column equals the sum along the horizontal row?<\/p>\n
This can be solved with any odd number in the centre square.<\/p>\n
When we put a number in the centre square the remainder must be divided into two equal parts.<\/p>\n
1+2+3+4+5+6+7+8+9 = 45<\/p>\n
IF we have an odd number in the centre square we will have an even sum left. If we put\u00a0 9 in the centre square the remaining numbers add up to 36. So there should be 18 in each arm along with the centre 9<\/p>\n<\/div>\n<\/div>
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/Screenshot-2022-10-19-at-15.22.37.png\" "\\"Screenshot")
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Counting Counties<\/h4>\n<\/div>\n\n
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Do you know all the counties of Ireland?<\/p>\n
Our map is a strange one. It doesn\u2019t represent the real shape and size of the counties, but shows how many other counties they border (with the connecting line).<\/p>\n
Can you find all the counties on our map and fill in their names?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/Counting-Counties-1.png\" "\\"Counting")
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An Ezee Puzzle<\/strong><\/h4>\n\n
These moving coin puzzles were popularised by the great English puzzler Henry Dudeney (1857-1930). They can be played with coins or counters or any objects that make two distinct sets of four.<\/p>\n
The aim of the E puzzle is to reverse the positions of the Green and Red counters in the grid by sliding them along.\u00a0<\/strong>There are rules of course to make it a challenge:<\/p>\n\n- No more than one piece can be in the same square at a time.<\/li>\n
- There is no jumping.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/Screenshot-2022-10-19-at-15.33.59.png\" "\\"Screenshot")
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Magic Squares<\/strong><\/h4>\n<\/div>\n\n
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A magic square is an arrangement of numbers in a grid where the numbers in each row, column and the diagonals all add up to the same amount. This amount is called the magic constant. The 3\u00d73 magic square shown uses the numbers 1-9. Can you figure out how to fill in the missing numbers?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/square-game-EL1910223.png\" "\\"square")
<\/span><\/div>The left-hand column adds up to 15, which tells us that all columns, rows and diagonals must add up to 15.<\/p>\n
So we see for top row 8 + 6 = 14 so the missing number must be 1. The middle column then is 1+ 9 = 10 so the centre number should be 5.<\/p>\n<\/div><\/div><\/div>
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Form a Closed Cube<\/h4>\n<\/div>\n\n
Which one of the following shapes, when folded along the lines shown will not form a closed cube?<\/p>\n<\/div>\n<\/div>\n<\/div>
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/Screenshot-2022-10-19-at-15.28.29.png\" "\\"Screenshot")
<\/span><\/div>Number 3 cannot fold into a box<\/p>\n<\/div><\/div><\/div><\/div><\/div>
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Brainteasers<\/h4>\n<\/div>\n\n
Errata: There were two errors in the short brain teasers. These were the fault of Maths Week not the Irish Times. Rough work got mixed up with the submitted text.) Thanks to a reader for pointing this out to us and apologies for any frustration caused.<\/p>\n
Question 10. The answer should be 4: two boys and two girls. This Mary has two brothers (twice as many) and one sister and John has two sisters (twice as many) and one brother.<\/p>\n
Question 13. Unluckily for us, the figures given in the question were wrong. This is a greater error as it may have caused frustration.<\/p>\n
The values should have been given as:<\/p>\n
A bag contains money in 5, 10 and 20 euro notes. You would have to take<\/p>\n
![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/irish-time-poster.png\")
<\/a><\/span><\/div>![](\"https:\/\/www.mathsweek.ie\/2026\/wp-content\/uploads\/2022\/10\/irish-time-poster2.png\")
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