DAY/DYDD/GIORNO/NAP 60:

T he Main Challenge

Read the information below to find each of these three different numbers:

  •  A is the only 2-digit square number that does not contain any odd digits
  •  B is the only 2-digit prime number with both its digits the same
  •  C is the only 2-digit cube number less than 50

Calculate the sum of A, B and C.

The 7puzzle Challenge

The playing board of the 7puzzle game is a 7-by-7 grid of 49 different numbers, ranging from up to 84.

The 4th & 6th rows contain the following fourteen numbers:

3   5   10   12   18   20   32   33   35   44   49   54   56   60

Which two numbers, when each is tripled, are also on the list?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every positive integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (or 4+1+1+1).

There are THREE ways of making 60 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which FOUR numbers is it possible to make from the list below?

7    14    21    28    35    42    49    56    63    70

#7TimesTable

The Target Challenge

Can you arrive at 60 by inserting 2, 3, 4 and 7 into the gaps on each line?

  •  (+◯)×(+◯) = 60
  •  (◯–◯)×◯× = 60
  •  ◯²+◯²+◯– = 60
  •  ◯²×◯²+◯– = 60

Answers can be found here.

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