# DAY/DYDD 39:

The Main Challenge

By allocating each letter of the English alphabet a numerical value as follows, A=1 B=2 C=3 . . . Z=26, the value of the word CAT would be 24, calculated by doing 3+1+20.

Following this rule, what is the value of the word ARITHMETIC?

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

Find three pairs of numbers that have a sum of 54.

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 just TWO ways of making 39 when using Lagrange’s Theorem. Can you find them both?

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?

60    61    62    63    64    65    66    67    68    69

#NumbersIn60s

The Target Challenge

Can you arrive at 39 by inserting 1, 3, 6 and 7 into the gaps on each line?

•  (◯+◯)×◯×◯ = 39
•  ◯²–(++◯) = 39
•  (◯–◯)×◯+◯ = 39

Answers can be found here.

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