These number puzzles work like crosswords, but some of the clues don't give you very much information! You must use logic to deduce the unique answer to each puzzle. You don't need great mathematical knowledge, just imaginative logic. It might be easier to print this page out and work on paper. Good luck!

**None of the answers start with the digit zero in ***any* of these puzzles.

**EXAMPLE**

ACROSS

1. More than three times 5 across

4. A square number (you won't need to list *all* three-digit square numbers to deduce this one!)

5. Divisible by 60

DOWN

1. All the digits in this number are even and different

2. The first digit of this number is the same as the first digit of 1 down

3. The digits in this number are in descending consecutive order

**SOLUTION**

- 5 across is divisible by 60, therefore its last digit is zero.
- 3 down can now be filled in as 210.
- A short list of possible square numbers for 4 across can now be deduced. Three-digit square numbers range from 10² (100) to 31² (961). Of those, only squares of numbers ending in 1 or 9 will end in the digit 1 (and so fit in to the puzzle), so the options are: 11² (121), 19² (361), 21² (441), 29² (841) and 31² (961).
- The first digit in 4 across must be even (because all digits in 1 down are even), so 121, 361 and 961 can be eliminated, leaving only two possible numbers for 4 across: 441 and 841 - so the middle digit must be four.
- 1 across is more than three times 5 across, so 5 across must be less than 999 divided by three (333). But the first digit of 5 across must be even (because all digits in 1 down are even), so it must be must be two. (None of the answers start with zero in any of these puzzles).
- 5 across is divisible by 60, so having deduced that its first digit is two, it must be 240.
- 1 across is therefore more than 720 (more than three times 5 across), but its first digit must be even (because all digits in 1 down are even), so its first digit must be eight.
- Two possibilities for 4 across were deduced earlier: 441 or 841. But each digit in 1 down is different, so 1 down cannot be 882 - it must be 842 (making 4 across 441).
- The first digit of 2 down is the same as the first digit of 1 down, so it is an eight, making 2 down 844 (and making 1 across 882).

The unique answer:

**HARD**

ACROSS

1. A Fibonacci number (the Fibonacci sequence is 1,1,2,3,5,8,13,21,34,etc. - each number is the sum of the previous two)

4. Each digit in this number is smaller than the last

5. Each digit in this number is different and prime

DOWN

1. Double this number, add two, then reverse the digits, and you get the same number

2. A Fibonacci number

3. Each digit in this number appears twice in the finished puzzle

**HARD**

ACROSS

1. The result of multiplying together the digits in 5 across

4. A factorial number (for example 24 is a factorial number because 24 = 4 factorial = 4x3x2x1)

5. The digits in this number add up to seventeen

DOWN

1. Five less than 2 down

2. Five more than 1 down

3. A number

**VERY HARD**

ACROSS

1. See 2 down

4. See 2 down

5. See 2 down

DOWN

1. A number

2. The lowest possible sum of 1 across, 4 across and 5 across (given the clues)

3. The answers in this puzzle contain only four different digits between them

**VERY HARD**

ACROSS

1. Twenty more than 4 across

4. Each digit in this number is different and divisible by three

5. The digits in this number add up to twelve

DOWN

1. A palindromic number

2. Half of 4 across

3. The digits in this number add up to twelve

**VERY HARD**

ACROSS

1. A number

4. A palindromic number

5. Seven times 3 down

DOWN

1. The digits in this number add up to fourteen

2. 5 across plus 3 down

3. One seventh of 5 across

**VERY HARD**

ACROSS

1. Each digit in this number is odd

4. Each digit in this number is different and prime

5. This number contains the same digits as 2 down, but in a different order

DOWN

1. The digits in this number add up to twenty-one

2. Each digit in this number is two more than the last

3. Divisible by 125

**VERY HARD**

ACROSS

1. Six times the square root of 3 down

4. The first two digits in this number are the same

5. Lots more than 1 down

DOWN

1. Lots less than 5 across

2. All the digits in this number are prime (although the number is not prime)

3. 1 down plus 2 down

**EXTREMELY HARD**

ACROSS

1. The digits in this number are in ascending consecutive order

4. Less than 2 down

5. This number backwards is half of 1 across

DOWN

1. One more than 1 across

2. The digits in this number add up to eighteen

3. Divisible by three

**EXTREMELY HARD**

ACROSS

1. The last two digits of this number are the same as the first two digits of 3 down

4. The middle digit of this number is the average of the other eight digits in this puzzle

5. The digits in this number are in ascending consecutive order

DOWN

1. Each digit in this number is two more than the last

2. An even number

3. Divisible by seven

**EXTREMELY HARD**

ACROSS

1. Convert the numbers in the grid to letters (A=1), and this answer will complete a word square (three words reading across and three downwards)

4. Each digit in this number is two more than the last

5. Five hundred more than 3 down

DOWN

1. The digits in this number do not add up to fourteen

2. All the digits in this number are odd

3. This number is halfway between 1 down and 1 across, rounded up to the nearest whole number

**EXTREMELY HARD**

ACROSS

1. The digits in this number add up to 22

5. There is only one odd digit in this number

6. Each digit in this number is two more than the last

7. The first pair of digits in this number are the same as the second pair, and they are all even

DOWN

1. The digits in this number add up to 27

2. This number is twice one of the other numbers in this puzzle

3. Over 100 more than 6 across

4. A power of two

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