# day/dydd 160 at 7puzzleblog.com T he Main Challenge

•  I am a 2-digit number,
•  My 1st digit is bigger than my 2nd digit,
•  I am less than 50,
•  I am an odd number,
•  I am not a prime number.

Which number am I? 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 1st & 5th rows contain the following fourteen numbers:

2   6   7   9   14   15   16   21   22   40   50   72   81   84

Which of the multiples of 10 listed above has more factors? 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 160, in TWO different ways, when using Lagrange’s Theorem. The Mathematically Possible Challenge

Using the three digits 35 and 8 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 160 by inserting 5810 and 12 into the gaps on each line?

•  ◯×◯+◯×◯ = 160
•  ◯²+×÷ = 160
•  ◯××(◯)² = 160   