# DAY/DYDD 116: Th e Main Challenge

All of the following 3-digit numbers are divisible by 3, but only one is also a multiple of 9. Which one?

237  276  303  336  495  528  582  660  744  771  888  939

[Note: Get in touch if you don’t know the quick trick.] 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 difference between the highest and lowest multiples of 7? 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 FOUR ways of making 116 when using Lagrange’s Theorem. Can you find them? The Mathematically Possible Challenge

Using 24 and 12 once each, with + – × ÷ available, which TWO numbers are NOT possible to make from the list below?

4    8    12    16    20    24    28    32    36    40

#4TimesTable

The Target Challenge

Can you arrive at 116 by inserting 2, 3, 4 and 9 into the gaps on each line?

•  (◯×◯+◯)×◯ = 116
•  ◯³+◯²+◯²³ = 116
•  ◯³×◯(◯+◯) = 116   