# Tutor Hunt Questions

“1) A water lily in a pond doubles its size every day and in 28 days it fills the whole pond. How long does it take to fill half the pond?

2) When was the last year which reads the same upside upside down?

3) The reflection of a clock shows 3.55 (five to four), what time is it really?

2) When was the last year which reads the same upside upside down?

3) The reflection of a clock shows 3.55 (five to four), what time is it really?

7 years ago

Maths Question asked by Zak

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1) 27 days - if on day 28 the lily is the same size of the pond, and it had doubled its size every day, it follows that the lily was half that size on day 27, half the size of the pond.
2) 1961 - There are several numbers that look the same when rotated upside down: 0, 1 & 8. There is also a pair which if rotated look like the other: 6 & 9.
3) 3:22 - Numbers can also be flipped upside down (vertically reflected) as opposed to rotated. In this instance 3 also looks the same upside down (in addition to 0, 1 & 8 as before). 6 & 9 no longer mimic each other the pair in this instance is 2 & 5. Although 2 & 5 written in standard fonts (as they are written here) are not exact mimics of each other when vertically reflected, this is the case with a traditional LCD digital clock display that constructs numbers by combination of 7 possible lines (as you can see below).
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## 7 Answers

Answer to question 1: 27 days,

Answer to question 2: 1691,

Answer to question 3: 9.05.

Answer to question 2: 1691,

Answer to question 3: 9.05.

1. 27 days. To formally solve this you can construct a geometric sequence but really it is a question of logic. If the water lily doubles in size each day, then the day before it fills the entire pond it must fill half (50%) of the pond. The next day it doubles in size: 2 x 50% = 100% of the pond covered.

2. 2002 (assuming you write the numbers using only straight lines, as they appear on a digital clock). Only 0s, 1s, 2s, 5s and 8s appear the same upside down. As the order of the numbers in in the year are also reversed, e.g. 2011 becomes 1102, the first number must be the same as the last number and the 2nd number must be the same as the 3rd number. The last year to fit these criteria was 2002.

3. 8.05. If you draw a line of symmetry down the middle of the clock you can reflect the minute hand and hour hand and find our the actual time.

2. 2002 (assuming you write the numbers using only straight lines, as they appear on a digital clock). Only 0s, 1s, 2s, 5s and 8s appear the same upside down. As the order of the numbers in in the year are also reversed, e.g. 2011 becomes 1102, the first number must be the same as the last number and the 2nd number must be the same as the 3rd number. The last year to fit these criteria was 2002.

3. 8.05. If you draw a line of symmetry down the middle of the clock you can reflect the minute hand and hour hand and find our the actual time.

If the water lily is doubling in size every day, then on the 27th day the pond will be half full. On the 28th day the lily will double in size again and the pond will be full, as the question states.