# DAY 292:

Today’s Challenge

Following on from DAY 240, here’s another one of the unique Keith Number challenges made famous by Mike Keith and similar to Fibonacci numbers.  If you like playing around with numbers, you’ll love having a go at this fun concept.

The 1st 2-digit Keith Number14, is worked out by following a pattern:

•    1   4   5   9   14

1+4=5; 4+5=9; 5+9=14 (the total arrives back to the original number).

The 2nd 2-digit Keith Number19, is worked out in a similar way:

•    1   9   10   19

1+9=10; 9+10=19 (the total again arrives back to the original number).

By following this pattern, the 3rd and 4th 2-digit Keith Numbers are 28 and 47:

•    2   8   10   18   28
•    4   7   11   18   29   47

but can you continue this process and find the only other two that are below 100?

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 & 3rd rows contain the following fourteen numbers:

8    13    17    25    28    36    42    45    48    55    63    64    66    80

What is the sum of the square numbers?

Make 292 Challenge

Can you arrive at 292 by inserting 2, 3, 4, 5 and 6 into the gaps below?

[◯³×◯²+(◯–◯)²]×◯ = 292