# day/dydd 148 at 7puzzleblog.com

T he Main Challenge

What is the lowest whole number that is NOT a multiple of 5, 6, 7, 11 or 13, nor a prime number, square number or cube number?

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 2nd & 6th rows contain the following fourteen numbers:

5   8   12   17   18   20   28   33   48   49   55   56   63   64

From the above list, what is the sum of the multiples of 7?

The Lagrange Challenge

Lagrange’s Four-Square Theorem states that every integer can be made by adding up to four square numbers.

For example, 7 can be made by 2²+1²+1²+1² (4+1+1+1).

Show how you can make 148, in EIGHT different ways, when using Lagrange’s Theorem.

The Mathematically Possible Challenge

Using the three digits 26 and 9 once each, with + – × ÷ available, which is the ONLY number it’s possible to make from the list below?

11    22    33    44    55    66    77    88    99    110

#11TimesTable

The Target Challenge

Can you arrive at 148 by inserting 4512 and 20 into the gaps on each line?

•  (◯+◯+◯)×◯ = 148
•  ◯×◯+◯×◯ = 148