The Main Challenge

There are two sections below, both containing ten letters, A-J.  Each letter is linked to a division calculation:

  • Section 1

D:9÷3  H:8÷2  B:12÷3  I:8÷4  A:4÷2  E:24÷6  G:15÷5  C:20÷4  F:25÷5  J:7÷7

  • Section 2

I:6÷2  G:6÷3  D:10÷2  E:12÷4  J:14÷7  B:20÷5  A:18÷6  C:10÷5  F:16÷4  H:15÷3

Which is the only letter to contain the same answer in both sections?

The 7puzzle Challenge

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

The 5th & 7th rows contain the following fourteen numbers:

4   6   7   11   16   21   24   27   30   50   70   77   81   84

How many pairs of numbers from the list have a sum of 88?

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 SIX ways of making 139 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 36 and 10 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

1    3    6    10    15    21    28    36    45    55


The Target Challenge

Can you arrive at 139 by inserting 3, 7, 9 and 11 into the gaps on each line?

  •  ◯×(◯+◯)+◯ = 139
  •  ◯²+◯×◯–◯² = 139

Answers can be found here.

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