A short introduction Cookie policy

Solution to: Pastor Petersen

The pastor's age is 49.

Explanation: first, we resolve 2450 into factors: 2450=2*5*5*7*7. These five prime factors can be assigned to the three women in the following 20 ways:

woman 1woman 2woman 3
112*5*5*7*7
125*5*7*7
12*55*7*7
12*5*57*7
12*5*5*77
12*75*5*7
12*5*75*7
12*5*7*75
12*7*75*5
255*7*7
25*57*7
25*5*77
25*75*7
2*557*7
2*55*77
2*755*7
2*75*57
2*5*577
2*5*757
2*7*755

This gives the following possible ages for the three women:

woman 1woman 2woman 3total age
1124502452
1212251228
110245256
15049100
13507358
114175190
17035106
14905496
19825124
25245252
2254972
2175776
23535184
1054964
1035752
1453554
1425746
507764
705782
9855108

As can be seen, there are two combinations that yield 64 as total age. All other totals occur only once. Since the teacher could not conclude how old each of the three women was based on the product and the sum, we conclude that the teacher must be 64. Therefore, the possible ages for the women are 5, 10, and 49, or 7, 7, and 50. Now we must use the second hint, which says that the teacher can work out how old the three women are if he knows that the oldest of the women is older than the pastor is. If the pastor would be younger than 49, the puzzle would still not be solvable, since the oldest woman is either 49 or 50. However, if the pastor would be older than 49, the oldest woman would not be older than the pastor is. Therefore, the pastor's age is 49.



back to the puzzle

Copyright © 1996-2016. RJE-productions. All rights reserved. No part of this website may be published, in any form or by any means, without the prior permission of the authors.
This website uses cookies. By further use of this website, or by clicking on 'Continue', you give permission for the use of cookies. If you want more information, look at our cookie policy.Continue