# DAY/DYDD/GIORNO/NAP 118:

Th e Main Challenge

Instead of being numbered 1-12, a traditional clock had √1√4√9 . . . √144 around its circumference. Every digit is represented on the clock, except one.

What is this missing digit?

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 & 6th rows contain the following fourteen numbers:

5   6   7   12   16   18   20   21   33   49   50   56   81   84

What is the sum of the factors of 40 listed above?

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 SEVEN ways of making 118 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which THREE numbers is it possible to make from the list below?

6    12    18    24    30    36    42    48    54    60

#6TimesTable

The Target Challenge

Can you arrive at 118 by inserting 1, 2, 4 and 5 into the gaps on each line?

•  ◯³+◯–◯×◯ = 118
•  (◯³–◯×◯)×◯ = 118