Number Play: questions with answers

Count only the taller children standing right next to each child. For B the count is 2, for C it is 0, for D it is 2, and for E it is 0. Only child D says the number that matches this count.

The speech bubble is wrong because an end child has only one neighbour, the child next to it. That child is taller than the end child, so the end child should say 1. Taller children farther along the row are not neighbours, so they do not count.

The odd positions must be local peaks, so each odd-position number must be greater than its adjacent even-position number or numbers. The row 5, 1, 4, 2, 3 alternates high and low values and uses each number from 1 to 5 exactly once.

The largest value in the row is 100, in Cell B. Every neighbour of that cell is another value in the same row, and every other row value is less than 100. Therefore Cell B is definitely a supercell.

The border has 8 boxes and the centre has 1 boxes. The border sum is 8 × 50 = 400. The centre sum is 1 × 125 = 125. The total is 400 + 125 = 525.

The 3 labelled boxes add up to 3 × 45 = 135. Subtract this from the total: 360 - 135 = 225.

The labelled ticks are 3 equal intervals apart. Their difference is 6, so each interval is 2. From the left labelled tick to ?, move 1 interval(s) to the right, giving 2012.

The two labelled ticks are 4 intervals apart. Their difference is 20, so the step size between consecutive ticks is 20 / 4 = 5.

Add the digits of the number under the ?. For 49, the digit sum is 4 + 9 = 13.

There is no largest whole number with digit sum 14. The numbers 59, 590, and 5900 all have digit sum 14. Adding another zero at the right gives 59000, which is larger again and still has digit sum 14.

The interval includes both endpoints. Therefore the count is 9999 - 1000 + 1 = 9000.

Put each digit in the place its card names. The ten-thousands digit is 9, the thousands digit is 4, the hundreds digit is 8, the tens digit is 1, and the units digit is 6. So the number is 94816.

In the Kaprekar procedure, each new result is used for the next subtraction. From 6382, the results shown are 6264 and then 4176. Using the digits of 4176 gives 7641 - 1467 = 6174, so ? is 6174.

22 is even, so we halve it: 22 ÷ 2 = 11. Checking the next arrow, 11 is odd, so it goes to 34. This matches the next box, so the missing term is 11.

The original estimate and the reliable count differ by 12 litres. Since 12 is not more than 15, the original estimate was reasonable even though it was not exact.