# DAY/DYDD/PÄIVÄ/NAP 62

T he Main Challenge

When listing the FIVE 3-digit cube numbers, all digits from 1 to 9 are represented, except one. Which digit is missing?

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

What is the difference between the two multiples of 9?

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 62 when using Lagrange’s Theorem. Can you find them?

The Mathematically Possible Challenge

Using 16 and once each, with + – × ÷ available, which is the ONLY number it is possible to make from the list below?

9    18    27    36    45    54    63    72    81    90

#9TimesTable

The Target Challenge

Can you arrive at 62 by inserting 2, 4, 6 and 9 into the gaps on each line?

•  (◯+◯)×◯+ = 62
•  (◯+◯)×◯– = 62
•  (◯+◯)×◯+◯² = 62