Even, odd, even, odd…

The idea

The counting numbers alternate between even and odd, so of any two consecutive numbers one is always even and the other always odd.

Martin and Maria

Martin and Maria were born exactly one year apart. Maria is 52 and Martin is 51: their ages are consecutive numbers.

Look at any two consecutive numbers, like 51 and 52. What is true?

• Both can be even
• Both can be odd
• One is even and the other is odd

Walk along the strip

Tap a number to check it and its next-door neighbour. Colours: even is blue, odd is orange. Can you find two neighbours with the same colour?

Even, odd, even, odd

The counting numbers alternate between even and odd: odd, even, odd, even and so on. So a number and the next one always have different parity.

The counting numbers alternate between even and odd. In any two consecutive numbers, one is always even and the other is always odd.

• Consecutive numbers | Parity
• 7, 8 | odd, even
• 51, 52 | odd, even
• 100, 101 | even, odd

Notes

The counting numbers alternate between even and odd. In any two consecutive numbers, one is always even and the other is always odd.

Check yourself

Which pair of numbers could be consecutive?

Count 32, 33, 34, … up to 41 (ten numbers). How many of them are even?

Answer: 5

32, 34, 36, 38, 40 are even: 5 numbers. The other five (33, 35, 37, 39, 41) are odd.

The number 1,000 is even. What can we say about 999 and 1,001?

Houses on a road are numbered 1 to 25. The odd-numbered houses are on the left side. How many houses are on the left side?

Answer: 13

The odd numbers 1, 3, 5, …, 25 are 13 numbers. There are 12 even ones (2, 4, …, 24).

• 24 and 26. Both are even. 25 comes between them, so they are two steps apart, not consecutive.
• 27 and 29. Both are odd. 28 comes between them, so they are two steps apart.
• 50 and 52. Both are even. 51 comes between them.
• 13 and 14 — correct. Yes! 13 is odd and 14 is even: one of each.
• Both are odd — correct. Yes! Parity alternates, so both neighbours of an even number are odd.
• 999 is odd and 1,001 is even. The number after an even number is odd. So 1,001 is odd too.
• Both are even. A number next to an even number cannot be even: parity alternates.