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3 down is a multiple of 101, so its middle digit must be 0:
The clue 4 across now tells us that the units digit of today's number (ie 1 across) is 5 or 0. As 3 down cannot begin with 0, it must be 5.
3 down is a multiple of 101:
The sum of the digits of today's number is at most 9+9+5 = 23, so 1 down starts with a 1 or 2. This means that the sum of the digits of today's number is at most 2 + 9 + 5 = 16, so 1 down must start with a 1:
Two times today's number (ie 4 across) must start with a 2 or 3. If it started with 2, then the sum of the digits of today's number (1 down) would be 12, so today's number would be 165. The product of
the digits of today's number (5 across) would be 30. This is not possible as 5 across ends in 5. The first digit of 4 across must therefore be a 3:
The sum of the digits of today's number is 13, and we can fill in the rest using the clues for 4 and 5 across:
Therefore, today's number is 175.
