Puzzles
24 December
3 and 5 are both factors of 2025, and 3 and 5 are the only two prime numbers that are factors of 2025.
What is the largest three-digit number that has both 3 and 5 as factors and no other prime numbers as factors?
23 December
153 is equal to the sum of the cubes of its digits: 13 + 53 + 33.
There are three other three-digit numbers that are equal to the sum of the cubes of their digits. What is the largest of these numbers?
22 December
Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums 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.
Today's number is the product of the numbers in the red boxes.
| × | + | = 11 | |||
| × | ÷ | + | |||
| ÷ | ÷ | = 1 | |||
| – | – | ÷ | |||
| + | – | = 1 | |||
| = 1 | = 0 | = 1 |
20 December
A number is called a perfect power if it is equal to nk for some integer n and some integer k > 1. 2025 is a perfect power (452)
and 23 more than 2025 is also a perfect power (211).
What is the only three-digit perfect power that is 29 less than another perfect power?
19 December
Eve uses the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write five square numbers (using each digit exactly once). What is largest square number that she made?
18 December
There are 5 different ways to make a set of numbers between 1 and 5 such that the smallest number in the set is equal to the number of numbers in the set. These 5 sets are: {1}, {2, 3}, {2, 4}, {2, 5} and {3, 4, 5}.
How many ways are there to make a set of numbers between 1 and 14 such that the smallest number in the set is equal to the number of numbers in the set?
17 December
A sequence of zeros and ones can be reduced by writing a 0 or 1 under each pair of numbers: 1 is written if the numbers are the same, 0 is written if they are not.
This process can be repeated until there is a single number. For example, if we start with the sequence 1, 1, 1, 0, 1 (of length 5), we get:
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
The final digit is a 1.
How many sequences of zeros and ones of length 10 are there that when reduced lead to the final digit being a 1?
16 December
Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums 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.
Today's number is the product of the numbers in the red boxes.
| – | ÷ | = 1 | |||
| ÷ | + | × | |||
| × | – | = 37 | |||
| × | ÷ | ÷ | |||
| + | + | = 17 | |||
| = 2 | = 1 | = 2 |
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