Great Granddad is very proud of his telegram from the Queen
congratulating him on his hundredth birthday and he has friends who
are even older than he is... When was he born?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3
grid so that all the rows and columns add up to a prime number. How
many different solutions can you find?
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
Class 2YP at Madras College carried out their own investigation
based on this problem and came up with some intriguing and
surprising results. One problem they set themselves was to find the
number of ways of writing 1999 as the sum of three odd numbers. We
leave this for you as a challenge now. The account of 2YP's work
will be published on 1 September.
Solutions accompanied by some explanation were sent in by Kang
Hong Joo, age 14 of the Chinese High School, Singapore, by Daniel
King and Chao Yu, year 7, Comberton Village College Cambridge and
by class 8x from the Key Stage 3 Maths Club at Strabane Grammar
School. Well done everyone who found all these solutions and also
proved that it is impossible to find 6 odd numbers adding up to
Class 8X said:
"We knew every solution had to contain a 1 since the next odd
number is 3 and 4*3 = 12 and 8*3 = 24.
It is impossible to get a total of 15 with 6 odd numbers since
adding 2 odd numbers gives an even number so if we add them in
pairs we get 3 even numbers and adding even numbers gives an even
This is Kang Hong Joo's solution:
3 ways to add 4 odd numbers to get 10
11 ways to add 8 odd numbers to get 20
It is impossible to add 6 odd numbers to get 15 because the sum
of an even number of odd numbers will always be an even number. The
diagram shows how pairs of odd numbers give even numbers so the
total must be even.