Puzzles

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/16. This is the sum of 5 unit fractions (the numerators are 1).

In how many different ways can 1 be written as the sum of 5 unit fractions? (the same fractions in a different order are considered the same sum.)

Put the digits 1 to 9 (using each digit once) in the boxes so that the three digit numbers formed (reading left to right and top to bottom) have the desired properties written by their rows and columns.

Today's number is the multiple of 6 formed in the left hand column.

In March, I posted the puzzle One Hundred Factorial, which asked how many zeros 100! ends with.

What is the smallest number, n, such that n! ends with 50 zeros?

Today's number is four thirds of the average (mean) of the answers for 13th, 14th, 15th and 16th December.

If the numbers 1 to 7 are arranged 7,1,2,6,3,4,5 then each number is either larger than or a factor of the number before it.

How many ways can the numbers 1 to 7 be arranged to that each number is either larger than or a factor of the number before it?

What is the only palindromic three digit prime number which is also palindromic when written in binary?

Put the digits 1 to 9 (using each digit once) in the boxes so that the three digit numbers formed (reading left to right and top to bottom) have the desired properties written by their rows and columns.

The row marked sum is equal to the sum of the other two rows. The column marked sum is equal to the sum of the other two columns.

Today's number is the largest three digit number in this grid.

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums reading across and down are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10.

The answer is the product of the digits in the red boxes.