# DAY/DYDD/PÄIVÄ/NAP 18

The Main Challenge

All nine numbers from 21 to 29 inclusive must be allocated to a letter below so that each allocated number satisfies the condition given on the line:

•  (a)  even number,
•  (b)  factor of 144,
•  (c)  power of 3,
•  (d)  prime number,
•  (e)  digits which differ by 1,
•  (f)  exactly 3 factors,
•  (g)  multiple of 7,
•  (h)  equal to the sum of all its factors (except the number itself),
•  (i)   2nd digit is greater than its 1st digit.

But, the numbers 21 to 29 should only appear once each above!

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 & 7th rows contain the following fourteen numbers:

2   4   9   11   14   15   22   24   27   30   40   70   72   77

Which odd number, when 21 is added to it, becomes a square number?

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

The Mathematically Possible Challenge

Using 56 and once each, with + – × ÷ available, which are the only TWO numbers 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 18 by inserting 2, 3, 4 and 6 into the gaps on each line?

•  ◯×◯–◯×◯ = 18
•  ◯÷◯×◯×◯² = 18
•  (◯÷◯)³×√◯÷◯ = 18