# DAY/DYDD 38:

The Main Challenge

Firstly, allocate each letter of the English alphabet a numerical value as follows, A=1 B=2 C=3 . . . Z=26.  If the value of the word DOG is 26 by calculating 4+15+7, for example, which TWO of the following 3-letter words have the same value?

AXE  AND  BUT  COT  EAR  MOP  SAW  TOP  WOK  ZOO

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 1st & 4th rows contain the following fourteen numbers:

2   3   9   10   14   15   22   32   35   40   44   54   60   72

How many square numbers are present 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 38 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 26 and 11 once each, with + – × ÷ available, which are the only TWO numbers it is possible to make from the list below?

30    31    32    33    34    35    36    37    38    39

#NumbersIn30s

The Target Challenge

Can you arrive at 38 by inserting 4, 6, 8 and 10 into the gaps on each line?

•  ◯×◯+◯– = 38
•  ◯²–◯²+ = 38
•  ◯²+◯+◯–◯ = 38