Place value

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain why this works.

Explore a number pattern which has the same symmetries in different bases.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Replace each letter with a digit to make this addition correct.

Find the sum of all three-digit numbers each of whose digits is odd.

Can you substitute numbers for the letters in these sums?