# DAY/DYDD 168: T he Main Challenge

The two sections below both contain eight letters, A-H. Each letter has an addition calculation attached, all involving 2-digit numbers.

Which is the only letter that has exactly the same answer in both sections?

• Section 1

D:68+18   B:51+14   E:47+31   H:62+32   A:44+29   G:59+25   C:36+23   F:38+26

• Section 2

E:64+28   A:31+27   F:34+22   B:43+19   G:48+36   C:54+16   D:48+21   H:50+38 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 2nd & 7th rows contain the following fourteen numbers:

4   8   11   17   24   27   28   30   48   55   63   64   70   77

Which three different numbers have a total which is also present on the list? The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every 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).

Show how you can make 168, in FOUR different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using 46 and 10 once each, with + – × ÷ available, which are the only TWO numbers it is 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 168 by inserting 2, 4, 6 and 9 into the gaps on each line?

•  (◯–◯)×◯×◯ = 168
•  ◯³×◯–◯²×◯ = 168   